Solve 8x^2 6x = -5

Question

Solve the equation

x = - \frac{3 180}{12}

Alternative Form

x \approx - 0.470518

Evaluate

8 x^{2} \times 6 x = - 5

Multiply

More Steps

Evaluate

8 x^{2} \times 6 x

Multiply the terms

48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

48 x^{2 + 1}

Add the numbers

48 x^{3}

48 x^{3} = - 5

Divide both sides

\frac{48 x ^{3}}{48} = \frac{- 5}{48}

Divide the numbers

x^{3} = \frac{- 5}{48}

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

x^{3} = - \frac{5}{48}

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

3 x^{3} = 3 - \frac{5}{48}

Calculate

x = 3 - \frac{5}{48}

Solution

More Steps

Evaluate

3 - \frac{5}{48}

An odd root of a negative radicand is always a negative

- 3 \frac{5}{48}

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

- \frac{3 5}{3 48}

Simplify the radical expression

More Steps

Evaluate

348

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

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

- \frac{3 5}{2 3 6}

Multiply by the Conjugate

\frac{- 3 5 \times 3 6 ^{2}}{2 3 6 \times 3 6 ^{2}}

Simplify

\frac{- 3 5 \times 3 36}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 35 \times 336

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

- 3 5 \times 36

Calculate the product

- 3180

\frac{- 3 180}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

236 \times 3 6^{2}

Multiply the terms

2 \times 6

Multiply the terms

12

\frac{- 3 180}{12}

Calculate

- \frac{3 180}{12}

x = - \frac{3 180}{12}

Alternative Form

x \approx - 0.470518

Show Solution