Solve -6x^226x-65

Question

Simplify the expression

- 156 x^{3} - 65

Evaluate

- 6 x^{2} \times 26 x - 65

Solution

More Steps

Evaluate

- 6 x^{2} \times 26 x

Multiply the terms

- 156 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 156 x^{2 + 1}

Add the numbers

- 156 x^{3}

- 156 x^{3} - 65

Show Solution

Factor the expression

- 13 (12 x^{3} + 5)

Evaluate

- 6 x^{2} \times 26 x - 65

Multiply

More Steps

Evaluate

- 6 x^{2} \times 26 x

Multiply the terms

- 156 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 156 x^{2 + 1}

Add the numbers

- 156 x^{3}

- 156 x^{3} - 65

Solution

- 13 (12 x^{3} + 5)

Show Solution

Find the roots

x = - \frac{3 90}{6}

Alternative Form

x \approx - 0.746901

Evaluate

- 6 x^{2} \times 26 x - 65

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

- 6 x^{2} \times 26 x - 65 = 0

Multiply

More Steps

Multiply the terms

- 6 x^{2} \times 26 x

Multiply the terms

- 156 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 156 x^{2 + 1}

Add the numbers

- 156 x^{3}

- 156 x^{3} - 65 = 0

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

- 156 x^{3} = 0 + 65

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

- 156 x^{3} = 65

Change the signs on both sides of the equation

156 x^{3} = - 65

Divide both sides

\frac{156 x ^{3}}{156} = \frac{- 65}{156}

Divide the numbers

x^{3} = \frac{- 65}{156}

Divide the numbers

More Steps

Evaluate

\frac{- 65}{156}

Cancel out the common factor 13

\frac{- 5}{12}

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

- \frac{5}{12}

x^{3} = - \frac{5}{12}

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

3 x^{3} = 3 - \frac{5}{12}

Calculate

x = 3 - \frac{5}{12}

Solution

More Steps

Evaluate

3 - \frac{5}{12}

An odd root of a negative radicand is always a negative

- 3 \frac{5}{12}

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

- \frac{3 5}{3 12}

Multiply by the Conjugate

\frac{- 3 5 \times 3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{- 3 5 \times 2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 35 \times 2318

Multiply the terms

- 390 \times 2

Use the commutative property to reorder the terms

- 2390

\frac{- 2 3 90}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 3 1 2^{2}

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

3 12 \times 1 2^{2}

Calculate the product

3 1 2^{3}

Reduce the index of the radical and exponent with 3

12

\frac{- 2 3 90}{12}

Cancel out the common factor 2

\frac{- 3 90}{6}

Calculate

- \frac{3 90}{6}

x = - \frac{3 90}{6}

Alternative Form

x \approx - 0.746901

Show Solution