Solve -x^2 6x-11 - ScanMath

Question

Simplify the expression

- 6 x^{3} - 11

Evaluate

- x^{2} \times 6 x - 11

Solution

More Steps

Evaluate

- x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 6

Add the numbers

- x^{3} \times 6

Use the commutative property to reorder the terms

- 6 x^{3}

- 6 x^{3} - 11

Show Solution

x = - \frac{3 396}{6}

Alternative Form

x \approx - 1.223903

Evaluate

- x^{2} \times 6 x - 11

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

- x^{2} \times 6 x - 11 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

- 6 x^{3} - 11 = 0

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

- 6 x^{3} = 0 + 11

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

- 6 x^{3} = 11

Change the signs on both sides of the equation

6 x^{3} = - 11

Divide both sides

\frac{6 x ^{3}}{6} = \frac{- 11}{6}

Divide the numbers

x^{3} = \frac{- 11}{6}

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

x^{3} = - \frac{11}{6}

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

3 x^{3} = 3 - \frac{11}{6}

Calculate

x = 3 - \frac{11}{6}

Solution

More Steps

Evaluate

3 - \frac{11}{6}

An odd root of a negative radicand is always a negative

- 3 \frac{11}{6}

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

- \frac{3 11}{3 6}

Multiply by the Conjugate

\frac{- 3 11 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{- 3 11 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 311 \times 336

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

- 3 11 \times 36

Calculate the product

- 3396

\frac{- 3 396}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{- 3 396}{6}

Calculate

- \frac{3 396}{6}

x = - \frac{3 396}{6}

Alternative Form

x \approx - 1.223903

Show Solution