Solve 2y^2-(2-y)^2

Question

Simplify the expression

y^{2} - 4 + 4 y

Show Solution

y_{1} = - 2 - 22, y_{2} = - 2 + 22

Alternative Form

y_{1} \approx - 4.828427, y_{2} \approx 0.828427

Evaluate

2 y^{2} - (2 - y)^{2}

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

2 y^{2} - (2 - y)^{2} = 0

Calculate

More Steps

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

Rewrite in standard form

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

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

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

Simplify the expression

More Steps

y = \frac{- 4 \pm 32}{2}

Simplify the radical expression

More Steps

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

Separate the equation into 2 possible cases

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

Simplify the expression

More Steps

y = - 2 + 22 y = \frac{- 4 - 4 2}{2}

Simplify the expression

More Steps

y = - 2 + 22 y = - 2 - 22

Solution

y_{1} = - 2 - 22, y_{2} = - 2 + 22

Alternative Form

y_{1} \approx - 4.828427, y_{2} \approx 0.828427

Show Solution