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

Evaluate

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

Substitute a= 2,b= - 2 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 ( - 1 )}{2 \times 2}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 ( - 1 )}{4}

Simplify the expression

More Steps

x = \frac{2 \pm 12}{4}

Simplify the radical expression

More Steps

x = \frac{2 \pm 2 3}{4}

Separate the equation into 2 possible cases

x = \frac{2 + 2 3}{4} x = \frac{2 - 2 3}{4}

Simplify the expression

More Steps

x = \frac{1 + 3}{2} x = \frac{2 - 2 3}{4}

Simplify the expression

More Steps

x = \frac{1 + 3}{2} x = \frac{1 - 3}{2}

Solution

x_{1} = \frac{1 - 3}{2}, x_{2} = \frac{1 + 3}{2}

Alternative Form

x_{1} \approx - 0.366025, x_{2} \approx 1.366025

Solve the quadratic equation