Solve -7x^2 2x-1=0

Question

Solve the equation

x = - \frac{3 196}{14}

Alternative Form

x \approx - 0.414913

Evaluate

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

Multiply

More Steps

Evaluate

- 7 x^{2} \times 2 x

Multiply the terms

- 14 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 14 x^{2 + 1}

Add the numbers

- 14 x^{3}

- 14 x^{3} - 1 = 0

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

- 14 x^{3} = 0 + 1

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

- 14 x^{3} = 1

Change the signs on both sides of the equation

14 x^{3} = - 1

Divide both sides

\frac{14 x ^{3}}{14} = \frac{- 1}{14}

Divide the numbers

x^{3} = \frac{- 1}{14}

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

x^{3} = - \frac{1}{14}

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

3 x^{3} = 3 - \frac{1}{14}

Calculate

x = 3 - \frac{1}{14}

Solution

More Steps

Evaluate

3 - \frac{1}{14}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{14}

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

- \frac{3 1}{3 14}

Simplify the radical expression

- \frac{1}{3 14}

Multiply by the Conjugate

\frac{- 3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{- 3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{- 3 196}{14}

Calculate

- \frac{3 196}{14}

x = - \frac{3 196}{14}

Alternative Form

x \approx - 0.414913

Show Solution