4g^2-3g-2=0

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Solution for 4g^2-3g-2=0 equation: 


Simplifying
4g2 + -3g + -2 = 0

Reorder the terms:
-2 + -3g + 4g2 = 0

Solving
-2 + -3g + 4g2 = 0

Solving for variable 'g'.

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

Divide each side by '4'.
-0.5 + -0.75g + g2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.75g + 0.5 + g2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.75g + g2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.75g + g2 = 0 + 0.5
-0.75g + g2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.75g + g2 = 0.5

The g term is -0.75g.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75g + 0.140625 + g2 = 0.5 + 0.140625

Reorder the terms:
0.140625 + -0.75g + g2 = 0.5 + 0.140625

Combine like terms: 0.5 + 0.140625 = 0.640625
0.140625 + -0.75g + g2 = 0.640625

Factor a perfect square on the left side:
(g + -0.375)(g + -0.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(g + -0.375) equal to 0.80039053 and -0.80039053.


Subproblem 1
g + -0.375 = 0.80039053

Simplifying
g + -0.375 = 0.80039053

Reorder the terms:
-0.375 + g = 0.80039053

Solving
-0.375 + g = 0.80039053

Solving for variable 'g'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + g = 0.80039053 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + g = 0.80039053 + 0.375
g = 0.80039053 + 0.375

Combine like terms: 0.80039053 + 0.375 = 1.17539053
g = 1.17539053

Simplifying
g = 1.17539053


Subproblem 2
g + -0.375 = -0.80039053

Simplifying
g + -0.375 = -0.80039053

Reorder the terms:
-0.375 + g = -0.80039053

Solving
-0.375 + g = -0.80039053

Solving for variable 'g'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + g = -0.80039053 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + g = -0.80039053 + 0.375
g = -0.80039053 + 0.375

Combine like terms: -0.80039053 + 0.375 = -0.42539053
g = -0.42539053

Simplifying
g = -0.42539053


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {1.17539053, -0.42539053}

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