y^2+12.25y-180=0

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Solution for y^2+12.25y-180=0 equation: 


Simplifying
y2 + 12.25y + -180 = 0

Reorder the terms:
-180 + 12.25y + y2 = 0

Solving
-180 + 12.25y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 12.25y + 180 + y2 = 0 + 180

Reorder the terms:
-180 + 180 + 12.25y + y2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 12.25y + y2 = 0 + 180
12.25y + y2 = 0 + 180

Combine like terms: 0 + 180 = 180
12.25y + y2 = 180

The y term is 12.25y.  Take half its coefficient (6.125).
Square it (37.515625) and add it to both sides.

Add '37.515625' to each side of the equation.
12.25y + 37.515625 + y2 = 180 + 37.515625

Reorder the terms:
37.515625 + 12.25y + y2 = 180 + 37.515625

Combine like terms: 180 + 37.515625 = 217.515625
37.515625 + 12.25y + y2 = 217.515625

Factor a perfect square on the left side:
(y + 6.125)(y + 6.125) = 217.515625

Calculate the square root of the right side: 14.748410931

Break this problem into two subproblems by setting 
(y + 6.125) equal to 14.748410931 and -14.748410931.


Subproblem 1
y + 6.125 = 14.748410931

Simplifying
y + 6.125 = 14.748410931

Reorder the terms:
6.125 + y = 14.748410931

Solving
6.125 + y = 14.748410931

Solving for variable 'y'.

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

Add '-6.125' to each side of the equation.
6.125 + -6.125 + y = 14.748410931 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + y = 14.748410931 + -6.125
y = 14.748410931 + -6.125

Combine like terms: 14.748410931 + -6.125 = 8.623410931
y = 8.623410931

Simplifying
y = 8.623410931


Subproblem 2
y + 6.125 = -14.748410931

Simplifying
y + 6.125 = -14.748410931

Reorder the terms:
6.125 + y = -14.748410931

Solving
6.125 + y = -14.748410931

Solving for variable 'y'.

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

Add '-6.125' to each side of the equation.
6.125 + -6.125 + y = -14.748410931 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + y = -14.748410931 + -6.125
y = -14.748410931 + -6.125

Combine like terms: -14.748410931 + -6.125 = -20.873410931
y = -20.873410931

Simplifying
y = -20.873410931


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.623410931, -20.873410931}

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