g^2-24g-47=0

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Solution for g^2-24g-47=0 equation: 


Simplifying
g2 + -24g + -47 = 0

Reorder the terms:
-47 + -24g + g2 = 0

Solving
-47 + -24g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -24g + 47 + g2 = 0 + 47

Reorder the terms:
-47 + 47 + -24g + g2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -24g + g2 = 0 + 47
-24g + g2 = 0 + 47

Combine like terms: 0 + 47 = 47
-24g + g2 = 47

The g term is -24g.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24g + 144 + g2 = 47 + 144

Reorder the terms:
144 + -24g + g2 = 47 + 144

Combine like terms: 47 + 144 = 191
144 + -24g + g2 = 191

Factor a perfect square on the left side:
(g + -12)(g + -12) = 191

Calculate the square root of the right side: 13.820274961

Break this problem into two subproblems by setting 
(g + -12) equal to 13.820274961 and -13.820274961.


Subproblem 1
g + -12 = 13.820274961

Simplifying
g + -12 = 13.820274961

Reorder the terms:
-12 + g = 13.820274961

Solving
-12 + g = 13.820274961

Solving for variable 'g'.

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

Add '12' to each side of the equation.
-12 + 12 + g = 13.820274961 + 12

Combine like terms: -12 + 12 = 0
0 + g = 13.820274961 + 12
g = 13.820274961 + 12

Combine like terms: 13.820274961 + 12 = 25.820274961
g = 25.820274961

Simplifying
g = 25.820274961


Subproblem 2
g + -12 = -13.820274961

Simplifying
g + -12 = -13.820274961

Reorder the terms:
-12 + g = -13.820274961

Solving
-12 + g = -13.820274961

Solving for variable 'g'.

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

Add '12' to each side of the equation.
-12 + 12 + g = -13.820274961 + 12

Combine like terms: -12 + 12 = 0
0 + g = -13.820274961 + 12
g = -13.820274961 + 12

Combine like terms: -13.820274961 + 12 = -1.820274961
g = -1.820274961

Simplifying
g = -1.820274961


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {25.820274961, -1.820274961}

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