Solve (3x^2 x-5)(2x^2-10x-7)

Question

Simplify the expression

6 x^{5} - 30 x^{4} - 21 x^{3} - 10 x^{2} + 50 x + 35

Evaluate

(3 x^{2} \times x - 5) (2 x^{2} - 10 x - 7)

Multiply

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Evaluate

3 x^{2} \times x

Multiply the terms with the same base by adding their exponents

3 x^{2 + 1}

Add the numbers

3 x^{3}

(3 x^{3} - 5) (2 x^{2} - 10 x - 7)

Apply the distributive property

3 x^{3} \times 2 x^{2} - 3 x^{3} \times 10 x - 3 x^{3} \times 7 - 5 \times 2 x^{2} - (- 5 \times 10 x) - (- 5 \times 7)

Multiply the terms

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Evaluate

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

Multiply the numbers

6 x^{3} \times x^{2}

Multiply the terms

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Evaluate

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

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 2}

Add the numbers

x^{5}

6 x^{5}

6 x^{5} - 3 x^{3} \times 10 x - 3 x^{3} \times 7 - 5 \times 2 x^{2} - (- 5 \times 10 x) - (- 5 \times 7)

Multiply the terms

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Evaluate

3 x^{3} \times 10 x

Multiply the numbers

30 x^{3} \times x

Multiply the terms

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Evaluate

x^{3} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 1}

Add the numbers

x^{4}

30 x^{4}

6 x^{5} - 30 x^{4} - 3 x^{3} \times 7 - 5 \times 2 x^{2} - (- 5 \times 10 x) - (- 5 \times 7)

Multiply the numbers

6 x^{5} - 30 x^{4} - 21 x^{3} - 5 \times 2 x^{2} - (- 5 \times 10 x) - (- 5 \times 7)

Multiply the numbers

6 x^{5} - 30 x^{4} - 21 x^{3} - 10 x^{2} - (- 5 \times 10 x) - (- 5 \times 7)

Multiply the numbers

6 x^{5} - 30 x^{4} - 21 x^{3} - 10 x^{2} - (- 50 x) - (- 5 \times 7)

Multiply the numbers

6 x^{5} - 30 x^{4} - 21 x^{3} - 10 x^{2} - (- 50 x) - (- 35)

Solution

6 x^{5} - 30 x^{4} - 21 x^{3} - 10 x^{2} + 50 x + 35

Show Solution

Find the roots

x_{1} = \frac{5 - 39}{2}, x_{2} = \frac{3 45}{3}, x_{3} = \frac{5 + 39}{2}

Alternative Form

x_{1} \approx - 0.622499, x_{2} \approx 1.185631, x_{3} \approx 5.622499

Evaluate

(3 x^{2} \times x - 5) (2 x^{2} - 10 x - 7)

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

(3 x^{2} \times x - 5) (2 x^{2} - 10 x - 7) = 0

Multiply

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Multiply the terms

3 x^{2} \times x

Multiply the terms with the same base by adding their exponents

3 x^{2 + 1}

Add the numbers

3 x^{3}

(3 x^{3} - 5) (2 x^{2} - 10 x - 7) = 0

Separate the equation into 2 possible cases

3 x^{3} - 5 = 0 2 x^{2} - 10 x - 7 = 0

Solve the equation

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Evaluate

3 x^{3} - 5 = 0

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

3 x^{3} = 0 + 5

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

3 x^{3} = 5

Divide both sides

\frac{3 x ^{3}}{3} = \frac{5}{3}

Divide the numbers

x^{3} = \frac{5}{3}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{5}{3}

Calculate

x = 3 \frac{5}{3}

Simplify the root

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Evaluate

3 \frac{5}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 5}{3 3}

Multiply by the Conjugate

\frac{3 5 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 5 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 45}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 45}{3}

x = \frac{3 45}{3}

x = \frac{3 45}{3} 2 x^{2} - 10 x - 7 = 0

Solve the equation

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Evaluate

2 x^{2} - 10 x - 7 = 0

Substitute a= 2,b= - 10 and c= - 7 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 2 ( - 7 )}{2 \times 2}

Simplify the expression

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 2 ( - 7 )}{4}

Simplify the expression

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Evaluate

(- 10)^{2} - 4 \times 2 (- 7)

Multiply

(- 10)^{2} - (- 56)

Rewrite the expression

1 0^{2} - (- 56)

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

1 0^{2} + 56

Evaluate the power

100 + 56

Add the numbers

156

x = \frac{10 \pm 156}{4}

Simplify the radical expression

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Evaluate

156

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 39

Write the number in exponential form with the base of 2

2^{2} \times 39

The root of a product is equal to the product of the roots of each factor

2^{2} \times 39

Reduce the index of the radical and exponent with 2

239

x = \frac{10 \pm 2 39}{4}

Separate the equation into 2 possible cases

x = \frac{10 + 2 39}{4} x = \frac{10 - 2 39}{4}

Simplify the expression

x = \frac{5 + 39}{2} x = \frac{10 - 2 39}{4}

Simplify the expression

x = \frac{5 + 39}{2} x = \frac{5 - 39}{2}

x = \frac{3 45}{3} x = \frac{5 + 39}{2} x = \frac{5 - 39}{2}

Solution

x_{1} = \frac{5 - 39}{2}, x_{2} = \frac{3 45}{3}, x_{3} = \frac{5 + 39}{2}

Alternative Form

x_{1} \approx - 0.622499, x_{2} \approx 1.185631, x_{3} \approx 5.622499

Show Solution