# Solve for y (y-5^2)=y(y-8)+11 (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
Simplify each term.
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
Simplify each term.
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
Move all terms containing y to the left side of the equation.
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 all terms to the left side of the equation and simplify.
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.
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

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