y^2-89y+114=0

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Solution for y^2-89y+114=0 equation: 


Simplifying
y2 + -89y + 114 = 0

Reorder the terms:
114 + -89y + y2 = 0

Solving
114 + -89y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-114' to each side of the equation.
114 + -89y + -114 + y2 = 0 + -114

Reorder the terms:
114 + -114 + -89y + y2 = 0 + -114

Combine like terms: 114 + -114 = 0
0 + -89y + y2 = 0 + -114
-89y + y2 = 0 + -114

Combine like terms: 0 + -114 = -114
-89y + y2 = -114

The y term is -89y.  Take half its coefficient (-44.5).
Square it (1980.25) and add it to both sides.

Add '1980.25' to each side of the equation.
-89y + 1980.25 + y2 = -114 + 1980.25

Reorder the terms:
1980.25 + -89y + y2 = -114 + 1980.25

Combine like terms: -114 + 1980.25 = 1866.25
1980.25 + -89y + y2 = 1866.25

Factor a perfect square on the left side:
(y + -44.5)(y + -44.5) = 1866.25

Calculate the square root of the right side: 43.200115741

Break this problem into two subproblems by setting 
(y + -44.5) equal to 43.200115741 and -43.200115741.


Subproblem 1
y + -44.5 = 43.200115741

Simplifying
y + -44.5 = 43.200115741

Reorder the terms:
-44.5 + y = 43.200115741

Solving
-44.5 + y = 43.200115741

Solving for variable 'y'.

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

Add '44.5' to each side of the equation.
-44.5 + 44.5 + y = 43.200115741 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + y = 43.200115741 + 44.5
y = 43.200115741 + 44.5

Combine like terms: 43.200115741 + 44.5 = 87.700115741
y = 87.700115741

Simplifying
y = 87.700115741


Subproblem 2
y + -44.5 = -43.200115741

Simplifying
y + -44.5 = -43.200115741

Reorder the terms:
-44.5 + y = -43.200115741

Solving
-44.5 + y = -43.200115741

Solving for variable 'y'.

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

Add '44.5' to each side of the equation.
-44.5 + 44.5 + y = -43.200115741 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + y = -43.200115741 + 44.5
y = -43.200115741 + 44.5

Combine like terms: -43.200115741 + 44.5 = 1.299884259
y = 1.299884259

Simplifying
y = 1.299884259


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {87.700115741, 1.299884259}

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