Solve -3x^2 6x-11=0

Question

Solve the equation

x = - \frac{3 132}{6}

Alternative Form

x \approx - 0.848607

Evaluate

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

Multiply

More Steps

Evaluate

- 3 x^{2} \times 6 x

Multiply the terms

- 18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 18 x^{2 + 1}

Add the numbers

- 18 x^{3}

- 18 x^{3} - 11 = 0

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

- 18 x^{3} = 0 + 11

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

- 18 x^{3} = 11

Change the signs on both sides of the equation

18 x^{3} = - 11

Divide both sides

\frac{18 x ^{3}}{18} = \frac{- 11}{18}

Divide the numbers

x^{3} = \frac{- 11}{18}

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

x^{3} = - \frac{11}{18}

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

3 x^{3} = 3 - \frac{11}{18}

Calculate

x = 3 - \frac{11}{18}

Solution

More Steps

Evaluate

3 - \frac{11}{18}

An odd root of a negative radicand is always a negative

- 3 \frac{11}{18}

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

- \frac{3 11}{3 18}

Multiply by the Conjugate

\frac{- 3 11 \times 3 1 8 ^{2}}{3 18 \times 3 1 8 ^{2}}

Simplify

\frac{- 3 11 \times 3 3 12}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 311 \times 3312

Multiply the terms

- 3132 \times 3

Use the commutative property to reorder the terms

- 33132

\frac{- 3 3 132}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

318 \times 3 1 8^{2}

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

3 18 \times 1 8^{2}

Calculate the product

3 1 8^{3}

Reduce the index of the radical and exponent with 3

18

\frac{- 3 3 132}{18}

Cancel out the common factor 3

\frac{- 3 132}{6}

Calculate

- \frac{3 132}{6}

x = - \frac{3 132}{6}

Alternative Form

x \approx - 0.848607

Show Solution