Solve 8x^3+12 - ScanMath

Question

Factor the expression

Factor

4 (2 x^{3} + 3)

Evaluate

8 x^{3} + 12

Solution

4 (2 x^{3} + 3)

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Find the roots of the algebra expression

x = - \frac{3 12}{2}

Alternative Form

x \approx - 1.144714

Evaluate

8 x^{3} + 12

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

8 x^{3} + 12 = 0

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

8 x^{3} = 0 - 12

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

8 x^{3} = - 12

Divide both sides

\frac{8 x ^{3}}{8} = \frac{- 12}{8}

Divide the numbers

x^{3} = \frac{- 12}{8}

Divide the numbers

More Steps

Evaluate

\frac{- 12}{8}

Cancel out the common factor 4

\frac{- 3}{2}

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

- \frac{3}{2}

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 - \frac{3}{2}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{2}

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

- \frac{3 3}{3 2}

Rewrite the expression

\frac{- 3 3}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{- 3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 33 \times 34

The product of roots with the same index is equal to the root of the product

- 3 3 \times 4

Calculate the product

- 312

\frac{- 3 12}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

The product of roots with the same index is equal to the root of the product

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{- 3 12}{2}

Calculate

- \frac{3 12}{2}

x = - \frac{3 12}{2}

Alternative Form

x \approx - 1.144714

Show Solution