Solve y^2 - 2y = 1

Evaluate

y^{2} - 2 y = 1

Move the expression to the left side

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

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

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

Simplify the expression

More Steps

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

Simplify the radical expression

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

Separate the equation into 2 possible cases

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

Simplify the expression

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

Simplify the expression

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y = 1 + 2 y = 1 - 2

Solution

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

Alternative Form

y_{1} \approx - 0.414214, y_{2} \approx 2.414214

Solve the quadratic equation