Solve -2x^2 2x-1=0

Question

- 2 x^{2} \times 2 x - 1 = 0

Solve the equation

x = - \frac{3 2}{2}

Alternative Form

x \approx - 0.629961

Evaluate

- 2 x^{2} \times 2 x - 1 = 0

Multiply

More Steps

Evaluate

- 2 x^{2} \times 2 x

Multiply the terms

- 4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 4 x^{2 + 1}

Add the numbers

- 4 x^{3}

- 4 x^{3} - 1 = 0

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

- 4 x^{3} = 0 + 1

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

- 4 x^{3} = 1

Change the signs on both sides of the equation

4 x^{3} = - 1

Divide both sides

\frac{4 x ^{3}}{4} = \frac{- 1}{4}

Divide the numbers

x^{3} = \frac{- 1}{4}

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

x^{3} = - \frac{1}{4}

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

3 x^{3} = 3 - \frac{1}{4}

Calculate

x = 3 - \frac{1}{4}

Solution

More Steps

Evaluate

3 - \frac{1}{4}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{4}

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

- \frac{3 1}{3 4}

Simplify the radical expression

- \frac{1}{3 4}

Multiply by the Conjugate

\frac{- 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{- 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{- 2 3 2}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{- 2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{- 1}{2 ^{2 - 1}}

Subtract the terms

\frac{- 1}{2 ^{1}}

Simplify

\frac{- 1}{2}

\frac{- 3 2}{2}

Calculate

- \frac{3 2}{2}

x = - \frac{3 2}{2}

Alternative Form

x \approx - 0.629961

Show Solution