(y-8)(y-8)-28=0

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Solution for (y-8)(y-8)-28=0 equation:


Simplifying
(y + -8)(y + -8) + -28 = 0

Reorder the terms:
(-8 + y)(y + -8) + -28 = 0

Reorder the terms:
(-8 + y)(-8 + y) + -28 = 0

Multiply (-8 + y) * (-8 + y)
(-8(-8 + y) + y(-8 + y)) + -28 = 0
((-8 * -8 + y * -8) + y(-8 + y)) + -28 = 0
((64 + -8y) + y(-8 + y)) + -28 = 0
(64 + -8y + (-8 * y + y * y)) + -28 = 0
(64 + -8y + (-8y + y2)) + -28 = 0

Combine like terms: -8y + -8y = -16y
(64 + -16y + y2) + -28 = 0

Reorder the terms:
64 + -28 + -16y + y2 = 0

Combine like terms: 64 + -28 = 36
36 + -16y + y2 = 0

Solving
36 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -16y + -36 + y2 = 0 + -36

Reorder the terms:
36 + -36 + -16y + y2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -16y + y2 = 0 + -36
-16y + y2 = 0 + -36

Combine like terms: 0 + -36 = -36
-16y + y2 = -36

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 = -36 + 64

Reorder the terms:
64 + -16y + y2 = -36 + 64

Combine like terms: -36 + 64 = 28
64 + -16y + y2 = 28

Factor a perfect square on the left side:
(y + -8)(y + -8) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(y + -8) equal to 5.291502622 and -5.291502622.

Subproblem 1

y + -8 = 5.291502622 Simplifying y + -8 = 5.291502622 Reorder the terms: -8 + y = 5.291502622 Solving -8 + y = 5.291502622 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 = 5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + y = 5.291502622 + 8 y = 5.291502622 + 8 Combine like terms: 5.291502622 + 8 = 13.291502622 y = 13.291502622 Simplifying y = 13.291502622

Subproblem 2

y + -8 = -5.291502622 Simplifying y + -8 = -5.291502622 Reorder the terms: -8 + y = -5.291502622 Solving -8 + y = -5.291502622 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 = -5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + y = -5.291502622 + 8 y = -5.291502622 + 8 Combine like terms: -5.291502622 + 8 = 2.708497378 y = 2.708497378 Simplifying y = 2.708497378

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.291502622, 2.708497378}

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