Solve (3x - 1)(-2x^24x - 7)

Question

Simplify the expression

- 24 x^{4} - 21 x + 8 x^{3} + 7

Evaluate

(3 x - 1) (- 2 x^{2} \times 4 x - 7)

Multiply

More Steps

Evaluate

- 2 x^{2} \times 4 x

Multiply the terms

- 8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 8 x^{2 + 1}

Add the numbers

- 8 x^{3}

(3 x - 1) (- 8 x^{3} - 7)

Apply the distributive property

3 x (- 8 x^{3}) - 3 x \times 7 - (- 8 x^{3}) - (- 7)

Multiply the terms

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Evaluate

3 x (- 8 x^{3})

Multiply the numbers

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Evaluate

3 (- 8)

Multiplying or dividing an odd number of negative terms equals a negative

- 3 \times 8

Multiply the numbers

- 24

- 24 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

- 24 x^{4}

- 24 x^{4} - 3 x \times 7 - (- 8 x^{3}) - (- 7)

Multiply the numbers

- 24 x^{4} - 21 x - (- 8 x^{3}) - (- 7)

When there is - in front of an expression in parentheses change the sign of each term of the expression and remove the parentheses

- 24 x^{4} - 21 x + 8 x^{3} - (- 7)

Solution

- 24 x^{4} - 21 x + 8 x^{3} + 7

Show Solution

Find the roots

x_{1} = - \frac{3 7}{2}, x_{2} = \frac{1}{3}

Alternative Form

x_{1} \approx - 0.956466, x_{2} = 0. \dot{3}

Evaluate

(3 x - 1) (- 2 x^{2} \times 4 x - 7)

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

(3 x - 1) (- 2 x^{2} \times 4 x - 7) = 0

Multiply

More Steps

Multiply the terms

- 2 x^{2} \times 4 x

Multiply the terms

- 8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 8 x^{2 + 1}

Add the numbers

- 8 x^{3}

(3 x - 1) (- 8 x^{3} - 7) = 0

Separate the equation into 2 possible cases

3 x - 1 = 0 - 8 x^{3} - 7 = 0

Solve the equation

More Steps

Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = \frac{1}{3} - 8 x^{3} - 7 = 0

Solve the equation

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Evaluate

- 8 x^{3} - 7 = 0

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

- 8 x^{3} = 0 + 7

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

- 8 x^{3} = 7

Change the signs on both sides of the equation

8 x^{3} = - 7

Divide both sides

\frac{8 x ^{3}}{8} = \frac{- 7}{8}

Divide the numbers

x^{3} = \frac{- 7}{8}

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

x^{3} = - \frac{7}{8}

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

3 x^{3} = 3 - \frac{7}{8}

Calculate

x = 3 - \frac{7}{8}

Simplify the root

More Steps

Evaluate

3 - \frac{7}{8}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{8}

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

- \frac{3 7}{3 8}

Simplify the radical expression

- \frac{3 7}{2}

x = - \frac{3 7}{2}

x = \frac{1}{3} x = - \frac{3 7}{2}

Solution

x_{1} = - \frac{3 7}{2}, x_{2} = \frac{1}{3}

Alternative Form

x_{1} \approx - 0.956466, x_{2} = 0. \dot{3}

Show Solution