g^2-3g-7=0

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Solution for g^2-3g-7=0 equation:


Simplifying
g2 + -3g + -7 = 0

Reorder the terms:
-7 + -3g + g2 = 0

Solving
-7 + -3g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3g + 7 + g2 = 0 + 7

Reorder the terms:
-7 + 7 + -3g + g2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3g + g2 = 0 + 7
-3g + g2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3g + g2 = 7

The g term is -3g.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3g + 2.25 + g2 = 7 + 2.25

Reorder the terms:
2.25 + -3g + g2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3g + g2 = 9.25

Factor a perfect square on the left side:
(g + -1.5)(g + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(g + -1.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
g + -1.5 = 3.041381265

Simplifying
g + -1.5 = 3.041381265

Reorder the terms:
-1.5 + g = 3.041381265

Solving
-1.5 + g = 3.041381265

Solving for variable 'g'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + g = 3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + g = 3.041381265 + 1.5
g = 3.041381265 + 1.5

Combine like terms: 3.041381265 + 1.5 = 4.541381265
g = 4.541381265

Simplifying
g = 4.541381265


Subproblem 2
g + -1.5 = -3.041381265

Simplifying
g + -1.5 = -3.041381265

Reorder the terms:
-1.5 + g = -3.041381265

Solving
-1.5 + g = -3.041381265

Solving for variable 'g'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + g = -3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + g = -3.041381265 + 1.5
g = -3.041381265 + 1.5

Combine like terms: -3.041381265 + 1.5 = -1.541381265
g = -1.541381265

Simplifying
g = -1.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {4.541381265, -1.541381265}

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