Solve 4y^2 - 4y -1

Evaluate

4 y^{2} - 4 y - 1

To find the roots of the expression,set the expression equal to 0

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

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

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

Simplify the expression

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

Simplify the expression

More Steps

y = \frac{4 \pm 32}{8}

Simplify the radical expression

More Steps

y = \frac{4 \pm 4 2}{8}

Separate the equation into 2 possible cases

y = \frac{4 + 4 2}{8} y = \frac{4 - 4 2}{8}

Simplify the expression

More Steps

y = \frac{1 + 2}{2} y = \frac{4 - 4 2}{8}

Simplify the expression

More Steps

y = \frac{1 + 2}{2} y = \frac{1 - 2}{2}

Solution

y_{1} = \frac{1 - 2}{2}, y_{2} = \frac{1 + 2}{2}

Alternative Form

y_{1} \approx - 0.207107, y_{2} \approx 1.207107

Find the roots