24g^2+88g-48=0

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Solution for 24g^2+88g-48=0 equation: 


Simplifying
24g2 + 88g + -48 = 0

Reorder the terms:
-48 + 88g + 24g2 = 0

Solving
-48 + 88g + 24g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + 11g + 3g2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-6 + 11g + 3g2)' equal to zero and attempt to solve:

Simplifying
-6 + 11g + 3g2 = 0

Solving
-6 + 11g + 3g2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-2 + 3.666666667g + g2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3.666666667g + 2 + g2 = 0 + 2

Reorder the terms:
-2 + 2 + 3.666666667g + g2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3.666666667g + g2 = 0 + 2
3.666666667g + g2 = 0 + 2

Combine like terms: 0 + 2 = 2
3.666666667g + g2 = 2

The g term is 3.666666667g.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667g + 3.361111114 + g2 = 2 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667g + g2 = 2 + 3.361111114

Combine like terms: 2 + 3.361111114 = 5.361111114
3.361111114 + 3.666666667g + g2 = 5.361111114

Factor a perfect square on the left side:
(g + 1.833333334)(g + 1.833333334) = 5.361111114

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(g + 1.833333334) equal to 2.315407332 and -2.315407332.


Subproblem 1
g + 1.833333334 = 2.315407332

Simplifying
g + 1.833333334 = 2.315407332

Reorder the terms:
1.833333334 + g = 2.315407332

Solving
1.833333334 + g = 2.315407332

Solving for variable 'g'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + g = 2.315407332 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + g = 2.315407332 + -1.833333334
g = 2.315407332 + -1.833333334

Combine like terms: 2.315407332 + -1.833333334 = 0.482073998
g = 0.482073998

Simplifying
g = 0.482073998


Subproblem 2
g + 1.833333334 = -2.315407332

Simplifying
g + 1.833333334 = -2.315407332

Reorder the terms:
1.833333334 + g = -2.315407332

Solving
1.833333334 + g = -2.315407332

Solving for variable 'g'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + g = -2.315407332 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + g = -2.315407332 + -1.833333334
g = -2.315407332 + -1.833333334

Combine like terms: -2.315407332 + -1.833333334 = -4.148740666
g = -4.148740666

Simplifying
g = -4.148740666


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.482073998, -4.148740666}
Solution
g = {0.482073998, -4.148740666}

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