Solve 2x^2-4x-1=0

Evaluate

2 x^{2} - 4 x - 1 = 0

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

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

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{4 \pm 24}{4}

Simplify the radical expression

More Steps

x = \frac{4 \pm 2 6}{4}

Separate the equation into 2 possible cases

x = \frac{4 + 2 6}{4} x = \frac{4 - 2 6}{4}

Simplify the expression

More Steps

x = \frac{2 + 6}{2} x = \frac{4 - 2 6}{4}

Simplify the expression

More Steps

x = \frac{2 + 6}{2} x = \frac{2 - 6}{2}

Solution

x_{1} = \frac{2 - 6}{2}, x_{2} = \frac{2 + 6}{2}

Alternative Form

x_{1} \approx - 0.224745, x_{2} \approx 2.224745

Solve the quadratic equation