Solve y(10-y) = 20

Evaluate

y (10 - y) = 20

Expand the expression

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10 y - y^{2} = 20

Move the expression to the left side

10 y - y^{2} - 20 = 0

Rewrite in standard form

- y^{2} + 10 y - 20 = 0

Multiply both sides

y^{2} - 10 y + 20 = 0

Substitute a= 1,b= - 10 and c= 20 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 20}{2}

Simplify the expression

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y = \frac{10 \pm 20}{2}

Simplify the radical expression

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y = \frac{10 \pm 2 5}{2}

Separate the equation into 2 possible cases

y = \frac{10 + 2 5}{2} y = \frac{10 - 2 5}{2}

Simplify the expression

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y = 5 + 5 y = \frac{10 - 2 5}{2}

Simplify the expression

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y = 5 + 5 y = 5 - 5

Solution

y_{1} = 5 - 5, y_{2} = 5 + 5

Alternative Form

y_{1} \approx 2.763932, y_{2} \approx 7.236068

Solve the quadratic equation