Solve -2x^2 135x-132

Question

Simplify the expression

- 270 x^{3} - 132

Evaluate

- 2 x^{2} \times 135 x - 132

Solution

More Steps

Evaluate

- 2 x^{2} \times 135 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} - 132

Show Solution

Factor the expression

- 6 (45 x^{3} + 22)

Evaluate

- 2 x^{2} \times 135 x - 132

Multiply

More Steps

Evaluate

- 2 x^{2} \times 135 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} - 132

Solution

- 6 (45 x^{3} + 22)

Show Solution

Find the roots

x = - \frac{3 1650}{15}

Alternative Form

x \approx - 0.787777

Evaluate

- 2 x^{2} \times 135 x - 132

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

- 2 x^{2} \times 135 x - 132 = 0

Multiply

More Steps

Multiply the terms

- 2 x^{2} \times 135 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} - 132 = 0

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

- 270 x^{3} = 0 + 132

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

- 270 x^{3} = 132

Change the signs on both sides of the equation

270 x^{3} = - 132

Divide both sides

\frac{270 x ^{3}}{270} = \frac{- 132}{270}

Divide the numbers

x^{3} = \frac{- 132}{270}

Divide the numbers

More Steps

Evaluate

\frac{- 132}{270}

Cancel out the common factor 6

\frac{- 22}{45}

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

- \frac{22}{45}

x^{3} = - \frac{22}{45}

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

3 x^{3} = 3 - \frac{22}{45}

Calculate

x = 3 - \frac{22}{45}

Solution

More Steps

Evaluate

3 - \frac{22}{45}

An odd root of a negative radicand is always a negative

- 3 \frac{22}{45}

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

- \frac{3 22}{3 45}

Multiply by the Conjugate

\frac{- 3 22 \times 3 4 5 ^{2}}{3 45 \times 3 4 5 ^{2}}

Simplify

\frac{- 3 22 \times 3 3 75}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 322 \times 3375

Multiply the terms

- 31650 \times 3

Use the commutative property to reorder the terms

- 331650

\frac{- 3 3 1650}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 3 4 5^{2}

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

3 45 \times 4 5^{2}

Calculate the product

3 4 5^{3}

Reduce the index of the radical and exponent with 3

45

\frac{- 3 3 1650}{45}

Cancel out the common factor 3

\frac{- 3 1650}{15}

Calculate

- \frac{3 1650}{15}

x = - \frac{3 1650}{15}

Alternative Form

x \approx - 0.787777

Show Solution