(y+8)(y+8)-80=0

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Solution for (y+8)(y+8)-80=0 equation:


Simplifying
(y + 8)(y + 8) + -80 = 0

Reorder the terms:
(8 + y)(y + 8) + -80 = 0

Reorder the terms:
(8 + y)(8 + y) + -80 = 0

Multiply (8 + y) * (8 + y)
(8(8 + y) + y(8 + y)) + -80 = 0
((8 * 8 + y * 8) + y(8 + y)) + -80 = 0
((64 + 8y) + y(8 + y)) + -80 = 0
(64 + 8y + (8 * y + y * y)) + -80 = 0
(64 + 8y + (8y + y2)) + -80 = 0

Combine like terms: 8y + 8y = 16y
(64 + 16y + y2) + -80 = 0

Reorder the terms:
64 + -80 + 16y + y2 = 0

Combine like terms: 64 + -80 = -16
-16 + 16y + y2 = 0

Solving
-16 + 16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 16 + 64

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

Combine like terms: 16 + 64 = 80
64 + 16y + y2 = 80

Factor a perfect square on the left side:
(y + 8)(y + 8) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(y + 8) equal to 8.94427191 and -8.94427191.

Subproblem 1

y + 8 = 8.94427191 Simplifying y + 8 = 8.94427191 Reorder the terms: 8 + y = 8.94427191 Solving 8 + y = 8.94427191 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 = 8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + y = 8.94427191 + -8 y = 8.94427191 + -8 Combine like terms: 8.94427191 + -8 = 0.94427191 y = 0.94427191 Simplifying y = 0.94427191

Subproblem 2

y + 8 = -8.94427191 Simplifying y + 8 = -8.94427191 Reorder the terms: 8 + y = -8.94427191 Solving 8 + y = -8.94427191 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 = -8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + y = -8.94427191 + -8 y = -8.94427191 + -8 Combine like terms: -8.94427191 + -8 = -16.94427191 y = -16.94427191 Simplifying y = -16.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.94427191, -16.94427191}

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