(y-8)(y-8)-72=0

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Solution for (y-8)(y-8)-72=0 equation: 


Simplifying
(y + -8)(y + -8) + -72 = 0

Reorder the terms:
(-8 + y)(y + -8) + -72 = 0

Reorder the terms:
(-8 + y)(-8 + y) + -72 = 0

Multiply (-8 + y) * (-8 + y)
(-8(-8 + y) + y(-8 + y)) + -72 = 0
((-8 * -8 + y * -8) + y(-8 + y)) + -72 = 0
((64 + -8y) + y(-8 + y)) + -72 = 0
(64 + -8y + (-8 * y + y * y)) + -72 = 0
(64 + -8y + (-8y + y2)) + -72 = 0

Combine like terms: -8y + -8y = -16y
(64 + -16y + y2) + -72 = 0

Reorder the terms:
64 + -72 + -16y + y2 = 0

Combine like terms: 64 + -72 = -8
-8 + -16y + y2 = 0

Solving
-8 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -16y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + -16y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -16y + y2 = 0 + 8
-16y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-16y + y2 = 8

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = 8 + 64

Reorder the terms:
64 + -16y + y2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + -16y + y2 = 72

Factor a perfect square on the left side:
(y + -8)(y + -8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(y + -8) equal to 8.485281374 and -8.485281374.


Subproblem 1
y + -8 = 8.485281374

Simplifying
y + -8 = 8.485281374

Reorder the terms:
-8 + y = 8.485281374

Solving
-8 + y = 8.485281374

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + y = 8.485281374 + 8

Combine like terms: -8 + 8 = 0
0 + y = 8.485281374 + 8
y = 8.485281374 + 8

Combine like terms: 8.485281374 + 8 = 16.485281374
y = 16.485281374

Simplifying
y = 16.485281374


Subproblem 2
y + -8 = -8.485281374

Simplifying
y + -8 = -8.485281374

Reorder the terms:
-8 + y = -8.485281374

Solving
-8 + y = -8.485281374

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + y = -8.485281374 + 8

Combine like terms: -8 + 8 = 0
0 + y = -8.485281374 + 8
y = -8.485281374 + 8

Combine like terms: -8.485281374 + 8 = -0.485281374
y = -0.485281374

Simplifying
y = -0.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.485281374, -0.485281374}

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