g^2+7g+12.5=156.25

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Solution for g^2+7g+12.5=156.25 equation:


Simplifying
g2 + 7g + 12.5 = 156.25

Reorder the terms:
12.5 + 7g + g2 = 156.25

Solving
12.5 + 7g + g2 = 156.25

Solving for variable 'g'.

Reorder the terms:
12.5 + -156.25 + 7g + g2 = 156.25 + -156.25

Combine like terms: 12.5 + -156.25 = -143.75
-143.75 + 7g + g2 = 156.25 + -156.25

Combine like terms: 156.25 + -156.25 = 0.00
-143.75 + 7g + g2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '143.75' to each side of the equation.
-143.75 + 7g + 143.75 + g2 = 0.00 + 143.75

Reorder the terms:
-143.75 + 143.75 + 7g + g2 = 0.00 + 143.75

Combine like terms: -143.75 + 143.75 = 0.00
0.00 + 7g + g2 = 0.00 + 143.75
7g + g2 = 0.00 + 143.75

Combine like terms: 0.00 + 143.75 = 143.75
7g + g2 = 143.75

The g term is 7g.  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.
7g + 12.25 + g2 = 143.75 + 12.25

Reorder the terms:
12.25 + 7g + g2 = 143.75 + 12.25

Combine like terms: 143.75 + 12.25 = 156
12.25 + 7g + g2 = 156

Factor a perfect square on the left side:
(g + 3.5)(g + 3.5) = 156

Calculate the square root of the right side: 12.489995997

Break this problem into two subproblems by setting 
(g + 3.5) equal to 12.489995997 and -12.489995997.


Subproblem 1
g + 3.5 = 12.489995997

Simplifying
g + 3.5 = 12.489995997

Reorder the terms:
3.5 + g = 12.489995997

Solving
3.5 + g = 12.489995997

Solving for variable 'g'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + g = 12.489995997 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + g = 12.489995997 + -3.5
g = 12.489995997 + -3.5

Combine like terms: 12.489995997 + -3.5 = 8.989995997
g = 8.989995997

Simplifying
g = 8.989995997


Subproblem 2
g + 3.5 = -12.489995997

Simplifying
g + 3.5 = -12.489995997

Reorder the terms:
3.5 + g = -12.489995997

Solving
3.5 + g = -12.489995997

Solving for variable 'g'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + g = -12.489995997 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + g = -12.489995997 + -3.5
g = -12.489995997 + -3.5

Combine like terms: -12.489995997 + -3.5 = -15.989995997
g = -15.989995997

Simplifying
g = -15.989995997


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {8.989995997, -15.989995997}

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