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

Evaluate

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

Substitute a= 4,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 4 ( - 1 )}{2 \times 4}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 4 ( - 1 )}{8}

Simplify the expression

More Steps

x = \frac{2 \pm 20}{8}

Simplify the radical expression

More Steps

x = \frac{2 \pm 2 5}{8}

Separate the equation into 2 possible cases

x = \frac{2 + 2 5}{8} x = \frac{2 - 2 5}{8}

Simplify the expression

More Steps

x = \frac{1 + 5}{4} x = \frac{2 - 2 5}{8}

Simplify the expression

More Steps

x = \frac{1 + 5}{4} x = \frac{1 - 5}{4}

Solution

x_{1} = \frac{1 - 5}{4}, x_{2} = \frac{1 + 5}{4}

Alternative Form

x_{1} \approx - 0.309017, x_{2} \approx 0.809017

Solve the quadratic equation