(y-52)=y(y-8)+11

Since y is on the right side of the equation, switch the sides so it is on the left side of the equation.

y(y-8)+11=y-52

Apply the distributive property.

y⋅y+y⋅-8+11=y-52

Multiply y by y.

y2+y⋅-8+11=y-52

Move -8 to the left of y.

y2-8y+11=y-52

y2-8y+11=y-52

Raise 5 to the power of 2.

y2-8y+11=y-1⋅25

Multiply -1 by 25.

y2-8y+11=y-25

y2-8y+11=y-25

Subtract y from both sides of the equation.

y2-8y+11-y=-25

Subtract y from -8y.

y2-9y+11=-25

y2-9y+11=-25

Move 25 to the left side of the equation by adding it to both sides.

y2-9y+11+25=0

Add 11 and 25.

y2-9y+36=0

y2-9y+36=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-9, and c=36 into the quadratic formula and solve for y.

9±(-9)2-4⋅(1⋅36)2⋅1

Simplify the numerator.

Raise -9 to the power of 2.

y=9±81-4⋅(1⋅36)2⋅1

Multiply 36 by 1.

y=9±81-4⋅362⋅1

Multiply -4 by 36.

y=9±81-1442⋅1

Subtract 144 from 81.

y=9±-632⋅1

Rewrite -63 as -1(63).

y=9±-1⋅632⋅1

Rewrite -1(63) as -1⋅63.

y=9±-1⋅632⋅1

Rewrite -1 as i.

y=9±i⋅632⋅1

Rewrite 63 as 32⋅7.

Factor 9 out of 63.

y=9±i⋅9(7)2⋅1

Rewrite 9 as 32.

y=9±i⋅32⋅72⋅1

y=9±i⋅32⋅72⋅1

Pull terms out from under the radical.

y=9±i⋅(37)2⋅1

Move 3 to the left of i.

y=9±3i72⋅1

y=9±3i72⋅1

Multiply 2 by 1.

y=9±3i72

y=9±3i72

The final answer is the combination of both solutions.

y=9+3i72,9-3i72

Solve for y (y-5^2)=y(y-8)+11