y^2+8y-100=0

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Solution for y^2+8y-100=0 equation: 


Simplifying
y2 + 8y + -100 = 0

Reorder the terms:
-100 + 8y + y2 = 0

Solving
-100 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 8y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + 8y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 8y + y2 = 0 + 100
8y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
8y + y2 = 100

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 100 + 16

Reorder the terms:
16 + 8y + y2 = 100 + 16

Combine like terms: 100 + 16 = 116
16 + 8y + y2 = 116

Factor a perfect square on the left side:
(y + 4)(y + 4) = 116

Calculate the square root of the right side: 10.770329614

Break this problem into two subproblems by setting 
(y + 4) equal to 10.770329614 and -10.770329614.


Subproblem 1
y + 4 = 10.770329614

Simplifying
y + 4 = 10.770329614

Reorder the terms:
4 + y = 10.770329614

Solving
4 + y = 10.770329614

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 10.770329614 + -4

Combine like terms: 4 + -4 = 0
0 + y = 10.770329614 + -4
y = 10.770329614 + -4

Combine like terms: 10.770329614 + -4 = 6.770329614
y = 6.770329614

Simplifying
y = 6.770329614


Subproblem 2
y + 4 = -10.770329614

Simplifying
y + 4 = -10.770329614

Reorder the terms:
4 + y = -10.770329614

Solving
4 + y = -10.770329614

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -10.770329614 + -4

Combine like terms: 4 + -4 = 0
0 + y = -10.770329614 + -4
y = -10.770329614 + -4

Combine like terms: -10.770329614 + -4 = -14.770329614
y = -14.770329614

Simplifying
y = -14.770329614


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.770329614, -14.770329614}

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