y^2-88y-117=0

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Solution for y^2-88y-117=0 equation: 


Simplifying
y2 + -88y + -117 = 0

Reorder the terms:
-117 + -88y + y2 = 0

Solving
-117 + -88y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '117' to each side of the equation.
-117 + -88y + 117 + y2 = 0 + 117

Reorder the terms:
-117 + 117 + -88y + y2 = 0 + 117

Combine like terms: -117 + 117 = 0
0 + -88y + y2 = 0 + 117
-88y + y2 = 0 + 117

Combine like terms: 0 + 117 = 117
-88y + y2 = 117

The y term is -88y.  Take half its coefficient (-44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
-88y + 1936 + y2 = 117 + 1936

Reorder the terms:
1936 + -88y + y2 = 117 + 1936

Combine like terms: 117 + 1936 = 2053
1936 + -88y + y2 = 2053

Factor a perfect square on the left side:
(y + -44)(y + -44) = 2053

Calculate the square root of the right side: 45.310043037

Break this problem into two subproblems by setting 
(y + -44) equal to 45.310043037 and -45.310043037.


Subproblem 1
y + -44 = 45.310043037

Simplifying
y + -44 = 45.310043037

Reorder the terms:
-44 + y = 45.310043037

Solving
-44 + y = 45.310043037

Solving for variable 'y'.

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

Add '44' to each side of the equation.
-44 + 44 + y = 45.310043037 + 44

Combine like terms: -44 + 44 = 0
0 + y = 45.310043037 + 44
y = 45.310043037 + 44

Combine like terms: 45.310043037 + 44 = 89.310043037
y = 89.310043037

Simplifying
y = 89.310043037


Subproblem 2
y + -44 = -45.310043037

Simplifying
y + -44 = -45.310043037

Reorder the terms:
-44 + y = -45.310043037

Solving
-44 + y = -45.310043037

Solving for variable 'y'.

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

Add '44' to each side of the equation.
-44 + 44 + y = -45.310043037 + 44

Combine like terms: -44 + 44 = 0
0 + y = -45.310043037 + 44
y = -45.310043037 + 44

Combine like terms: -45.310043037 + 44 = -1.310043037
y = -1.310043037

Simplifying
y = -1.310043037


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {89.310043037, -1.310043037}

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