y^2-25y+134=0

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Solution for y^2-25y+134=0 equation: 


Simplifying
y2 + -25y + 134 = 0

Reorder the terms:
134 + -25y + y2 = 0

Solving
134 + -25y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-134' to each side of the equation.
134 + -25y + -134 + y2 = 0 + -134

Reorder the terms:
134 + -134 + -25y + y2 = 0 + -134

Combine like terms: 134 + -134 = 0
0 + -25y + y2 = 0 + -134
-25y + y2 = 0 + -134

Combine like terms: 0 + -134 = -134
-25y + y2 = -134

The y term is -25y.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25y + 156.25 + y2 = -134 + 156.25

Reorder the terms:
156.25 + -25y + y2 = -134 + 156.25

Combine like terms: -134 + 156.25 = 22.25
156.25 + -25y + y2 = 22.25

Factor a perfect square on the left side:
(y + -12.5)(y + -12.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(y + -12.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
y + -12.5 = 4.716990566

Simplifying
y + -12.5 = 4.716990566

Reorder the terms:
-12.5 + y = 4.716990566

Solving
-12.5 + y = 4.716990566

Solving for variable 'y'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + y = 4.716990566 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + y = 4.716990566 + 12.5
y = 4.716990566 + 12.5

Combine like terms: 4.716990566 + 12.5 = 17.216990566
y = 17.216990566

Simplifying
y = 17.216990566


Subproblem 2
y + -12.5 = -4.716990566

Simplifying
y + -12.5 = -4.716990566

Reorder the terms:
-12.5 + y = -4.716990566

Solving
-12.5 + y = -4.716990566

Solving for variable 'y'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + y = -4.716990566 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + y = -4.716990566 + 12.5
y = -4.716990566 + 12.5

Combine like terms: -4.716990566 + 12.5 = 7.783009434
y = 7.783009434

Simplifying
y = 7.783009434


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.216990566, 7.783009434}

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