Solve (x^5)(x-2)(x-(4-sqrt3)) ( x (4-sqrt3)) (x-(4 sq

Question

Simplify the expression

163 \times x^{10} - 12 x^{10} - 72 x^{9} - 603 \times x^{9} + 1104 x^{8} - 3283 \times x^{8} - 1824 x^{7} + 7683 \times x^{7}

Evaluate

x^{5} (x - 2) (x - (4 - 3)) (x (4 - 3)) (x - (43)) (x (43))

Remove the parentheses

x^{5} (x - 2) (x - (4 - 3)) x (4 - 3) (x - (43)) x \times 43

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{5} (x - 2) (x - 4 + 3) x (4 - 3) (x - (43)) x \times 43

Multiply the numbers

x^{5} (x - 2) (x - 4 + 3) x (4 - 3) (x - 43) x \times 43

Multiply the terms with the same base by adding their exponents

x^{5 + 1 + 1} (x - 2) (x - 4 + 3) (4 - 3) (x - 43) \times 43

Add the numbers

x^{7} (x - 2) (x - 4 + 3) (4 - 3) (x - 43) \times 43

Multiply the terms

More Steps

43 \times x^{7} (x - 2) (x - 4 + 3) (4 - 3) (x - 43)

Multiply the first two terms

More Steps

(163 - 12) x^{7} (x - 2) (x - 4 + 3) (x - 43)

Multiply the terms

More Steps

((163 - 12) x^{8} + (- 323 + 24) x^{7}) (x - 4 + 3) (x - 43)

Multiply the terms

More Steps

Evaluate

((163 - 12) x^{8} + (- 323 + 24) x^{7}) (x - 4 + 3)

Apply the distributive property

(163 - 12) x^{8} \times x - (163 - 12) x^{8} \times 4 + (163 - 12) x^{8} 3 + (- 323 + 24) x^{7} \times x - (- 323 + 24) x^{7} \times 4 + (- 323 + 24) x^{7} 3

Multiply the terms

More Steps

(163 - 12) x^{9} - (163 - 12) x^{8} \times 4 + (163 - 12) x^{8} 3 + (- 323 + 24) x^{7} \times x - (- 323 + 24) x^{7} \times 4 + (- 323 + 24) x^{7} 3

Multiply the numbers

More Steps

(163 - 12) x^{9} + (- 643 + 48) x^{8} + (163 - 12) x^{8} 3 + (- 323 + 24) x^{7} \times x - (- 323 + 24) x^{7} \times 4 + (- 323 + 24) x^{7} 3

Multiply the numbers

More Steps

(163 - 12) x^{9} + (- 643 + 48) x^{8} + (48 - 123) x^{8} + (- 323 + 24) x^{7} \times x - (- 323 + 24) x^{7} \times 4 + (- 323 + 24) x^{7} 3

Multiply the terms

More Steps

(163 - 12) x^{9} + (- 643 + 48) x^{8} + (48 - 123) x^{8} + (- 323 + 24) x^{8} - (- 323 + 24) x^{7} \times 4 + (- 323 + 24) x^{7} 3

Multiply the numbers

More Steps

(163 - 12) x^{9} + (- 643 + 48) x^{8} + (48 - 123) x^{8} + (- 323 + 24) x^{8} - (- 1283 + 96) x^{7} + (- 323 + 24) x^{7} 3

Multiply the numbers

More Steps

(163 - 12) x^{9} + (- 643 + 48) x^{8} + (48 - 123) x^{8} + (- 323 + 24) x^{8} - (- 1283 + 96) x^{7} + (- 96 + 243) x^{7}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

(163 - 12) x^{9} + (- 643 + 48) x^{8} + (48 - 123) x^{8} + (- 323 + 24) x^{8} + (1283 - 96) x^{7} + (- 96 + 243) x^{7}

((163 - 12) x^{9} + (- 643 + 48) x^{8} + (48 - 123) x^{8} + (- 323 + 24) x^{8} + (1283 - 96) x^{7} + (- 96 + 243) x^{7}) (x - 43)

Apply the distributive property

(163 - 12) x^{9} \times x - (163 - 12) x^{9} \times 43 + (- 643 + 48) x^{8} \times x - (- 643 + 48) x^{8} \times 43 + (48 - 123) x^{8} \times x - (48 - 123) x^{8} \times 43 + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the terms

More Steps

(163 - 12) x^{10} - (163 - 12) x^{9} \times 43 + (- 643 + 48) x^{8} \times x - (- 643 + 48) x^{8} \times 43 + (48 - 123) x^{8} \times x - (48 - 123) x^{8} \times 43 + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the numbers

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{8} \times x - (- 643 + 48) x^{8} \times 43 + (48 - 123) x^{8} \times x - (48 - 123) x^{8} \times 43 + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the terms

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 643 + 48) x^{8} \times 43 + (48 - 123) x^{8} \times x - (48 - 123) x^{8} \times 43 + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the numbers

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{8} \times x - (48 - 123) x^{8} \times 43 + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the terms

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} - (48 - 123) x^{8} \times 43 + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the numbers

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{8} \times x - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the terms

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} - (- 323 + 24) x^{8} \times 43 + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the numbers

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} - (- 384 + 963) x^{8} + (1283 - 96) x^{7} \times x - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the terms

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} - (- 384 + 963) x^{8} + (1283 - 96) x^{8} - (1283 - 96) x^{7} \times 43 + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the numbers

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} - (- 384 + 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{7} \times x - (- 96 + 243) x^{7} \times 43

Multiply the terms

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} - (- 384 + 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} - (- 96 + 243) x^{7} \times 43

Multiply the numbers

More Steps

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} - (- 768 + 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} - (- 384 + 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} - (- 3843 + 288) x^{7}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

(163 - 12) x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} + (768 - 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} + (- 192 + 483) x^{9} + (- 643 + 48) x^{9} + (768 - 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} + (- 643 + 48) x^{9} + (768 - 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + (768 - 1923) x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + (48 - 123) x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} + (- 1923 + 144) x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} + (- 323 + 24) x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 24 x^{9} + (384 - 963) x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 24 x^{9} + 384 x^{8} - 963 \times x^{8} + (1283 - 96) x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 24 x^{9} + 384 x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 96 x^{8} + (- 1536 + 3843) x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 24 x^{9} + 384 x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 96 x^{8} - 1536 x^{7} + 3843 \times x^{7} + (- 96 + 243) x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 24 x^{9} + 384 x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 96 x^{8} - 1536 x^{7} + 3843 \times x^{7} - 96 x^{8} + 243 \times x^{8} + (3843 - 288) x^{7}

Expand the expression

163 \times x^{10} - 12 x^{10} - 192 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 48 x^{9} + 768 x^{8} - 1923 \times x^{8} + 48 x^{9} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 24 x^{9} + 384 x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 96 x^{8} - 1536 x^{7} + 3843 \times x^{7} - 96 x^{8} + 243 \times x^{8} + 3843 \times x^{7} - 288 x^{7}

Add the terms

More Steps

163 \times x^{10} - 12 x^{10} - 72 x^{9} + 483 \times x^{9} - 643 \times x^{9} + 768 x^{8} - 1923 \times x^{8} - 123 \times x^{9} - 1923 \times x^{8} + 144 x^{8} - 323 \times x^{9} + 384 x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 96 x^{8} - 1536 x^{7} + 3843 \times x^{7} - 96 x^{8} + 243 \times x^{8} + 3843 \times x^{7} - 288 x^{7}

Subtract the terms

More Steps

163 \times x^{10} - 12 x^{10} - 72 x^{9} - 603 \times x^{9} + 768 x^{8} - 1923 \times x^{8} - 1923 \times x^{8} + 144 x^{8} + 384 x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 96 x^{8} - 1536 x^{7} + 3843 \times x^{7} - 96 x^{8} + 243 \times x^{8} + 3843 \times x^{7} - 288 x^{7}

Calculate the sum or difference

More Steps

163 \times x^{10} - 12 x^{10} - 72 x^{9} - 603 \times x^{9} + 1104 x^{8} - 1923 \times x^{8} - 1923 \times x^{8} - 963 \times x^{8} + 1283 \times x^{8} - 1536 x^{7} + 3843 \times x^{7} + 243 \times x^{8} + 3843 \times x^{7} - 288 x^{7}

Calculate the sum or difference

More Steps

163 \times x^{10} - 12 x^{10} - 72 x^{9} - 603 \times x^{9} + 1104 x^{8} - 3283 \times x^{8} - 1536 x^{7} + 3843 \times x^{7} + 3843 \times x^{7} - 288 x^{7}

Subtract the terms

More Steps

163 \times x^{10} - 12 x^{10} - 72 x^{9} - 603 \times x^{9} + 1104 x^{8} - 3283 \times x^{8} - 1824 x^{7} + 3843 \times x^{7} + 3843 \times x^{7}

Solution

More Steps

163 \times x^{10} - 12 x^{10} - 72 x^{9} - 603 \times x^{9} + 1104 x^{8} - 3283 \times x^{8} - 1824 x^{7} + 7683 \times x^{7}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2, x_{3} = 4 - 3, x_{4} = 43

Alternative Form

x_{1} = 0, x_{2} = 2, x_{3} \approx 2.267949, x_{4} \approx 6.928203

Evaluate

(x^{5}) (x - 2) (x - (4 - 3)) (x (4 - 3)) (x - (43)) (x (43))

To find the roots of the expression,set the expression equal to 0

(x^{5}) (x - 2) (x - (4 - 3)) (x (4 - 3)) (x - (43)) (x (43)) = 0

Calculate

x^{5} (x - 2) (x - (4 - 3)) (x (4 - 3)) (x - (43)) (x (43)) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{5} (x - 2) (x - 4 + 3) (x (4 - 3)) (x - (43)) (x (43)) = 0

Use the commutative property to reorder the terms

x^{5} (x - 2) (x - 4 + 3) (4 - 3) x (x - (43)) (x (43)) = 0

Multiply the numbers

x^{5} (x - 2) (x - 4 + 3) (4 - 3) x (x - 43) (x (43)) = 0

Multiply the numbers

x^{5} (x - 2) (x - 4 + 3) (4 - 3) x (x - 43) (x \times 43) = 0

Use the commutative property to reorder the terms

x^{5} (x - 2) (x - 4 + 3) (4 - 3) x (x - 43) \times 43 \times x = 0

Multiply the terms

More Steps

(163 - 12) x^{7} (x - 2) (x - 4 + 3) (x - 43) = 0

Elimination the left coefficient

x^{7} (x - 2) (x - 4 + 3) (x - 43) = 0

Separate the equation into 4 possible cases

x^{7} = 0 x - 2 = 0 x - 4 + 3 = 0 x - 43 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x - 2 = 0 x - 4 + 3 = 0 x - 43 = 0

Solve the equation

More Steps

x = 0 x = 2 x - 4 + 3 = 0 x - 43 = 0

Solve the equation

More Steps

x = 0 x = 2 x = 4 - 3 x - 43 = 0

Solve the equation

More Steps

x = 0 x = 2 x = 4 - 3 x = 43

Solution

x_{1} = 0, x_{2} = 2, x_{3} = 4 - 3, x_{4} = 43

Alternative Form

x_{1} = 0, x_{2} = 2, x_{3} \approx 2.267949, x_{4} \approx 6.928203

Show Solution