Solve -2x^(2) 11x-15

Question

Simplify the expression

- 22 x^{3} - 15

Evaluate

- 2 x^{2} \times 11 x - 15

Solution

More Steps

Evaluate

- 2 x^{2} \times 11 x

Multiply the terms

- 22 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 22 x^{2 + 1}

Add the numbers

- 22 x^{3}

- 22 x^{3} - 15

Show Solution

x = - \frac{3 7260}{22}

Alternative Form

x \approx - 0.880149

Evaluate

- 2 x^{2} \times 11 x - 15

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

- 2 x^{2} \times 11 x - 15 = 0

Multiply

More Steps

Multiply the terms

- 2 x^{2} \times 11 x

Multiply the terms

- 22 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 22 x^{2 + 1}

Add the numbers

- 22 x^{3}

- 22 x^{3} - 15 = 0

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

- 22 x^{3} = 0 + 15

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

- 22 x^{3} = 15

Change the signs on both sides of the equation

22 x^{3} = - 15

Divide both sides

\frac{22 x ^{3}}{22} = \frac{- 15}{22}

Divide the numbers

x^{3} = \frac{- 15}{22}

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

x^{3} = - \frac{15}{22}

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

3 x^{3} = 3 - \frac{15}{22}

Calculate

x = 3 - \frac{15}{22}

Solution

More Steps

Evaluate

3 - \frac{15}{22}

An odd root of a negative radicand is always a negative

- 3 \frac{15}{22}

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

- \frac{3 15}{3 22}

Multiply by the Conjugate

\frac{- 3 15 \times 3 2 2 ^{2}}{3 22 \times 3 2 2 ^{2}}

Simplify

\frac{- 3 15 \times 3 484}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 315 \times 3484

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

- 3 15 \times 484

Calculate the product

- 37260

\frac{- 3 7260}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

322 \times 3 2 2^{2}

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

3 22 \times 2 2^{2}

Calculate the product

3 2 2^{3}

Reduce the index of the radical and exponent with 3

22

\frac{- 3 7260}{22}

Calculate

- \frac{3 7260}{22}

x = - \frac{3 7260}{22}

Alternative Form

x \approx - 0.880149

Show Solution