y^2-26y+106.75=0

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Solution for y^2-26y+106.75=0 equation: 


Simplifying
y2 + -26y + 106.75 = 0

Reorder the terms:
106.75 + -26y + y2 = 0

Solving
106.75 + -26y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-106.75' to each side of the equation.
106.75 + -26y + -106.75 + y2 = 0 + -106.75

Reorder the terms:
106.75 + -106.75 + -26y + y2 = 0 + -106.75

Combine like terms: 106.75 + -106.75 = 0.00
0.00 + -26y + y2 = 0 + -106.75
-26y + y2 = 0 + -106.75

Combine like terms: 0 + -106.75 = -106.75
-26y + y2 = -106.75

The y term is -26y.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26y + 169 + y2 = -106.75 + 169

Reorder the terms:
169 + -26y + y2 = -106.75 + 169

Combine like terms: -106.75 + 169 = 62.25
169 + -26y + y2 = 62.25

Factor a perfect square on the left side:
(y + -13)(y + -13) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(y + -13) equal to 7.889866919 and -7.889866919.


Subproblem 1
y + -13 = 7.889866919

Simplifying
y + -13 = 7.889866919

Reorder the terms:
-13 + y = 7.889866919

Solving
-13 + y = 7.889866919

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = 7.889866919 + 13

Combine like terms: -13 + 13 = 0
0 + y = 7.889866919 + 13
y = 7.889866919 + 13

Combine like terms: 7.889866919 + 13 = 20.889866919
y = 20.889866919

Simplifying
y = 20.889866919


Subproblem 2
y + -13 = -7.889866919

Simplifying
y + -13 = -7.889866919

Reorder the terms:
-13 + y = -7.889866919

Solving
-13 + y = -7.889866919

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = -7.889866919 + 13

Combine like terms: -13 + 13 = 0
0 + y = -7.889866919 + 13
y = -7.889866919 + 13

Combine like terms: -7.889866919 + 13 = 5.110133081
y = 5.110133081

Simplifying
y = 5.110133081


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {20.889866919, 5.110133081}

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