Solve x^3 -8x^212x-9=0

Question

Solve the equation

x = - \frac{3 81225}{95}

Alternative Form

x \approx - 0.455869

Evaluate

x^{3} - 8 x^{2} \times 12 x - 9 = 0

Simplify

More Steps

Evaluate

x^{3} - 8 x^{2} \times 12 x - 9

Multiply

More Steps

Multiply the terms

- 8 x^{2} \times 12 x

Multiply the terms

- 96 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 1}

Add the numbers

- 96 x^{3}

x^{3} - 96 x^{3} - 9

Subtract the terms

More Steps

Evaluate

x^{3} - 96 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 96) x^{3}

Subtract the numbers

- 95 x^{3}

- 95 x^{3} - 9

- 95 x^{3} - 9 = 0

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

- 95 x^{3} = 0 + 9

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

- 95 x^{3} = 9

Change the signs on both sides of the equation

95 x^{3} = - 9

Divide both sides

\frac{95 x ^{3}}{95} = \frac{- 9}{95}

Divide the numbers

x^{3} = \frac{- 9}{95}

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

x^{3} = - \frac{9}{95}

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

3 x^{3} = 3 - \frac{9}{95}

Calculate

x = 3 - \frac{9}{95}

Solution

More Steps

Evaluate

3 - \frac{9}{95}

An odd root of a negative radicand is always a negative

- 3 \frac{9}{95}

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

- \frac{3 9}{3 95}

Multiply by the Conjugate

\frac{- 3 9 \times 3 9 5 ^{2}}{3 95 \times 3 9 5 ^{2}}

Simplify

\frac{- 3 9 \times 3 9025}{3 95 \times 3 9 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 39 \times 39025

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

- 3 9 \times 9025

Calculate the product

- 381225

\frac{- 3 81225}{3 95 \times 3 9 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

395 \times 3 9 5^{2}

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

3 95 \times 9 5^{2}

Calculate the product

3 9 5^{3}

Reduce the index of the radical and exponent with 3

95

\frac{- 3 81225}{95}

Calculate

- \frac{3 81225}{95}

x = - \frac{3 81225}{95}

Alternative Form

x \approx - 0.455869

Show Solution