y^2-28y-132=0

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Solution for y^2-28y-132=0 equation: 


Simplifying
y2 + -28y + -132 = 0

Reorder the terms:
-132 + -28y + y2 = 0

Solving
-132 + -28y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '132' to each side of the equation.
-132 + -28y + 132 + y2 = 0 + 132

Reorder the terms:
-132 + 132 + -28y + y2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + -28y + y2 = 0 + 132
-28y + y2 = 0 + 132

Combine like terms: 0 + 132 = 132
-28y + y2 = 132

The y term is -28y.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28y + 196 + y2 = 132 + 196

Reorder the terms:
196 + -28y + y2 = 132 + 196

Combine like terms: 132 + 196 = 328
196 + -28y + y2 = 328

Factor a perfect square on the left side:
(y + -14)(y + -14) = 328

Calculate the square root of the right side: 18.110770276

Break this problem into two subproblems by setting 
(y + -14) equal to 18.110770276 and -18.110770276.


Subproblem 1
y + -14 = 18.110770276

Simplifying
y + -14 = 18.110770276

Reorder the terms:
-14 + y = 18.110770276

Solving
-14 + y = 18.110770276

Solving for variable 'y'.

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

Add '14' to each side of the equation.
-14 + 14 + y = 18.110770276 + 14

Combine like terms: -14 + 14 = 0
0 + y = 18.110770276 + 14
y = 18.110770276 + 14

Combine like terms: 18.110770276 + 14 = 32.110770276
y = 32.110770276

Simplifying
y = 32.110770276


Subproblem 2
y + -14 = -18.110770276

Simplifying
y + -14 = -18.110770276

Reorder the terms:
-14 + y = -18.110770276

Solving
-14 + y = -18.110770276

Solving for variable 'y'.

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

Add '14' to each side of the equation.
-14 + 14 + y = -18.110770276 + 14

Combine like terms: -14 + 14 = 0
0 + y = -18.110770276 + 14
y = -18.110770276 + 14

Combine like terms: -18.110770276 + 14 = -4.110770276
y = -4.110770276

Simplifying
y = -4.110770276


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {32.110770276, -4.110770276}

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