Solve -4x^37x^2-29x^53(x^27)2

Question

Simplify the expression

- 28 x^{5} - 1218 x^{7}

Evaluate

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 (x^{2} \times 7) \times 2

Remove the parentheses

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 x^{2} \times 7 \times 2

Multiply

More Steps

Multiply the terms

- 4 x^{3} \times 7 x^{2}

Multiply the terms

- 28 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 28 x^{3 + 2}

Add the numbers

- 28 x^{5}

- 28 x^{5} - 29 x^{5} \times 3 x^{2} \times 7 \times 2

Solution

More Steps

Multiply the terms

29 x^{5} \times 3 x^{2} \times 7 \times 2

Multiply the terms

More Steps

Evaluate

29 \times 3 \times 7 \times 2

Multiply the terms

87 \times 7 \times 2

Multiply the terms

609 \times 2

Multiply the numbers

1218

1218 x^{5} \times x^{2}

Multiply the terms with the same base by adding their exponents

1218 x^{5 + 2}

Add the numbers

1218 x^{7}

- 28 x^{5} - 1218 x^{7}

Show Solution

Factor the expression

- 14 x^{5} (2 + 87 x^{2})

Evaluate

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 (x^{2} \times 7) \times 2

Remove the parentheses

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 x^{2} \times 7 \times 2

Multiply

More Steps

Multiply the terms

- 4 x^{3} \times 7 x^{2}

Multiply the terms

- 28 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 28 x^{3 + 2}

Add the numbers

- 28 x^{5}

- 28 x^{5} - 29 x^{5} \times 3 x^{2} \times 7 \times 2

Use the commutative property to reorder the terms

- 28 x^{5} - 29 x^{5} \times 3 \times 7 x^{2} \times 2

Multiply

More Steps

Multiply the terms

29 x^{5} \times 3 \times 7 x^{2} \times 2

Multiply the terms

More Steps

Evaluate

29 \times 3 \times 7 \times 2

Multiply the terms

87 \times 7 \times 2

Multiply the terms

609 \times 2

Multiply the numbers

1218

1218 x^{5} \times x^{2}

Multiply the terms with the same base by adding their exponents

1218 x^{5 + 2}

Add the numbers

1218 x^{7}

- 28 x^{5} - 1218 x^{7}

Rewrite the expression

- 14 x^{5} \times 2 - 14 x^{5} \times 87 x^{2}

Solution

- 14 x^{5} (2 + 87 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{174}{87} i, x_{2} = \frac{174}{87} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.15162 i, x_{2} \approx 0.15162 i, x_{3} = 0

Evaluate

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 (x^{2} \times 7) \times 2

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

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 (x^{2} \times 7) \times 2 = 0

Use the commutative property to reorder the terms

- 4 x^{3} \times 7 x^{2} - 29 x^{5} \times 3 \times 7 x^{2} \times 2 = 0

Multiply

More Steps

Multiply the terms

- 4 x^{3} \times 7 x^{2}

Multiply the terms

- 28 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 28 x^{3 + 2}

Add the numbers

- 28 x^{5}

- 28 x^{5} - 29 x^{5} \times 3 \times 7 x^{2} \times 2 = 0

Multiply

More Steps

Multiply the terms

29 x^{5} \times 3 \times 7 x^{2} \times 2

Multiply the terms

More Steps

Evaluate

29 \times 3 \times 7 \times 2

Multiply the terms

87 \times 7 \times 2

Multiply the terms

609 \times 2

Multiply the numbers

1218

1218 x^{5} \times x^{2}

Multiply the terms with the same base by adding their exponents

1218 x^{5 + 2}

Add the numbers

1218 x^{7}

- 28 x^{5} - 1218 x^{7} = 0

Factor the expression

- 14 x^{5} (2 + 87 x^{2}) = 0

Divide both sides

x^{5} (2 + 87 x^{2}) = 0

Separate the equation into 2 possible cases

x^{5} = 0 2 + 87 x^{2} = 0

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

x = 0 2 + 87 x^{2} = 0

Solve the equation

More Steps

Evaluate

2 + 87 x^{2} = 0

Move the constant to the right-hand side and change its sign

87 x^{2} = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

87 x^{2} = - 2

Divide both sides

\frac{87 x ^{2}}{87} = \frac{- 2}{87}

Divide the numbers

x^{2} = \frac{- 2}{87}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{2} = - \frac{2}{87}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm - \frac{2}{87}

Simplify the expression

More Steps

Evaluate

- \frac{2}{87}

Evaluate the power

\frac{2}{87} \times - 1

Evaluate the power

\frac{2}{87} \times i

Evaluate the power

\frac{174}{87} i

x = \pm \frac{174}{87} i

Separate the equation into 2 possible cases

x = \frac{174}{87} i x = - \frac{174}{87} i

x = 0 x = \frac{174}{87} i x = - \frac{174}{87} i

Solution

x_{1} = - \frac{174}{87} i, x_{2} = \frac{174}{87} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.15162 i, x_{2} \approx 0.15162 i, x_{3} = 0

Show Solution