g^2-5g+3=0

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Solution for g^2-5g+3=0 equation: 


Simplifying
g2 + -5g + 3 = 0

Reorder the terms:
3 + -5g + g2 = 0

Solving
3 + -5g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5g + -3 + g2 = 0 + -3

Reorder the terms:
3 + -3 + -5g + g2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5g + g2 = 0 + -3
-5g + g2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5g + g2 = -3

The g term is -5g.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5g + 6.25 + g2 = -3 + 6.25

Reorder the terms:
6.25 + -5g + g2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + -5g + g2 = 3.25

Factor a perfect square on the left side:
(g + -2.5)(g + -2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(g + -2.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
g + -2.5 = 1.802775638

Simplifying
g + -2.5 = 1.802775638

Reorder the terms:
-2.5 + g = 1.802775638

Solving
-2.5 + g = 1.802775638

Solving for variable 'g'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + g = 1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + g = 1.802775638 + 2.5
g = 1.802775638 + 2.5

Combine like terms: 1.802775638 + 2.5 = 4.302775638
g = 4.302775638

Simplifying
g = 4.302775638


Subproblem 2
g + -2.5 = -1.802775638

Simplifying
g + -2.5 = -1.802775638

Reorder the terms:
-2.5 + g = -1.802775638

Solving
-2.5 + g = -1.802775638

Solving for variable 'g'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + g = -1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + g = -1.802775638 + 2.5
g = -1.802775638 + 2.5

Combine like terms: -1.802775638 + 2.5 = 0.697224362
g = 0.697224362

Simplifying
g = 0.697224362


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {4.302775638, 0.697224362}

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