Solve 9x^2 30x=-25

Question

Solve the equation

x = - \frac{3 20}{6}

Alternative Form

x \approx - 0.452403

Evaluate

9 x^{2} \times 30 x = - 25

Multiply

More Steps

Evaluate

9 x^{2} \times 30 x

Multiply the terms

270 x^{2} \times x

Multiply the terms with the same base by adding their exponents

270 x^{2 + 1}

Add the numbers

270 x^{3}

270 x^{3} = - 25

Divide both sides

\frac{270 x ^{3}}{270} = \frac{- 25}{270}

Divide the numbers

x^{3} = \frac{- 25}{270}

Divide the numbers

More Steps

Evaluate

\frac{- 25}{270}

Cancel out the common factor 5

\frac{- 5}{54}

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

- \frac{5}{54}

x^{3} = - \frac{5}{54}

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

3 x^{3} = 3 - \frac{5}{54}

Calculate

x = 3 - \frac{5}{54}

Solution

More Steps

Evaluate

3 - \frac{5}{54}

An odd root of a negative radicand is always a negative

- 3 \frac{5}{54}

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

- \frac{3 5}{3 54}

Simplify the radical expression

More Steps

Evaluate

354

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

3 27 \times 2

Write the number in exponential form with the base of 3

3 3^{3} \times 2

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

3 3^{3} \times 32

Reduce the index of the radical and exponent with 3

332

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

Multiply by the Conjugate

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

Simplify

\frac{- 3 5 \times 3 4}{3 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 35 \times 34

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

- 3 5 \times 4

Calculate the product

- 320

\frac{- 3 20}{3 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

332 \times 3 2^{2}

Multiply the terms

3 \times 2

Multiply the terms

6

\frac{- 3 20}{6}

Calculate

- \frac{3 20}{6}

x = - \frac{3 20}{6}

Alternative Form

x \approx - 0.452403

Show Solution