y^2+12.25y-81=0

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Solution for y^2+12.25y-81=0 equation: 


Simplifying
y2 + 12.25y + -81 = 0

Reorder the terms:
-81 + 12.25y + y2 = 0

Solving
-81 + 12.25y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 12.25y + 81 + y2 = 0 + 81

Reorder the terms:
-81 + 81 + 12.25y + y2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 12.25y + y2 = 0 + 81
12.25y + y2 = 0 + 81

Combine like terms: 0 + 81 = 81
12.25y + y2 = 81

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 = 81 + 37.515625

Reorder the terms:
37.515625 + 12.25y + y2 = 81 + 37.515625

Combine like terms: 81 + 37.515625 = 118.515625
37.515625 + 12.25y + y2 = 118.515625

Factor a perfect square on the left side:
(y + 6.125)(y + 6.125) = 118.515625

Calculate the square root of the right side: 10.886488185

Break this problem into two subproblems by setting 
(y + 6.125) equal to 10.886488185 and -10.886488185.


Subproblem 1
y + 6.125 = 10.886488185

Simplifying
y + 6.125 = 10.886488185

Reorder the terms:
6.125 + y = 10.886488185

Solving
6.125 + y = 10.886488185

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 = 10.886488185 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + y = 10.886488185 + -6.125
y = 10.886488185 + -6.125

Combine like terms: 10.886488185 + -6.125 = 4.761488185
y = 4.761488185

Simplifying
y = 4.761488185


Subproblem 2
y + 6.125 = -10.886488185

Simplifying
y + 6.125 = -10.886488185

Reorder the terms:
6.125 + y = -10.886488185

Solving
6.125 + y = -10.886488185

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 = -10.886488185 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + y = -10.886488185 + -6.125
y = -10.886488185 + -6.125

Combine like terms: -10.886488185 + -6.125 = -17.011488185
y = -17.011488185

Simplifying
y = -17.011488185


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.761488185, -17.011488185}

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