y^2+7y+12.25=8

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Solution for y^2+7y+12.25=8 equation: 


Simplifying
y2 + 7y + 12.25 = 8

Reorder the terms:
12.25 + 7y + y2 = 8

Solving
12.25 + 7y + y2 = 8

Solving for variable 'y'.

Reorder the terms:
12.25 + -8 + 7y + y2 = 8 + -8

Combine like terms: 12.25 + -8 = 4.25
4.25 + 7y + y2 = 8 + -8

Combine like terms: 8 + -8 = 0
4.25 + 7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 7y + -4.25 + y2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 7y + y2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 7y + y2 = 0 + -4.25
7y + y2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
7y + y2 = -4.25

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = -4.25 + 12.25

Reorder the terms:
12.25 + 7y + y2 = -4.25 + 12.25

Combine like terms: -4.25 + 12.25 = 8
12.25 + 7y + y2 = 8

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(y + 3.5) equal to 2.828427125 and -2.828427125.


Subproblem 1
y + 3.5 = 2.828427125

Simplifying
y + 3.5 = 2.828427125

Reorder the terms:
3.5 + y = 2.828427125

Solving
3.5 + y = 2.828427125

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 2.828427125 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 2.828427125 + -3.5
y = 2.828427125 + -3.5

Combine like terms: 2.828427125 + -3.5 = -0.671572875
y = -0.671572875

Simplifying
y = -0.671572875


Subproblem 2
y + 3.5 = -2.828427125

Simplifying
y + 3.5 = -2.828427125

Reorder the terms:
3.5 + y = -2.828427125

Solving
3.5 + y = -2.828427125

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -2.828427125 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -2.828427125 + -3.5
y = -2.828427125 + -3.5

Combine like terms: -2.828427125 + -3.5 = -6.328427125
y = -6.328427125

Simplifying
y = -6.328427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.671572875, -6.328427125}

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