g^2-12g=29

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Solution for g^2-12g=29 equation:


Simplifying
g2 + -12g = 29

Reorder the terms:
-12g + g2 = 29

Solving
-12g + g2 = 29

Solving for variable 'g'.

Reorder the terms:
-29 + -12g + g2 = 29 + -29

Combine like terms: 29 + -29 = 0
-29 + -12g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -12g + 29 + g2 = 0 + 29

Reorder the terms:
-29 + 29 + -12g + g2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -12g + g2 = 0 + 29
-12g + g2 = 0 + 29

Combine like terms: 0 + 29 = 29
-12g + g2 = 29

The g term is -12g.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12g + 36 + g2 = 29 + 36

Reorder the terms:
36 + -12g + g2 = 29 + 36

Combine like terms: 29 + 36 = 65
36 + -12g + g2 = 65

Factor a perfect square on the left side:
(g + -6)(g + -6) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(g + -6) equal to 8.062257748 and -8.062257748.

Subproblem 1

g + -6 = 8.062257748 Simplifying g + -6 = 8.062257748 Reorder the terms: -6 + g = 8.062257748 Solving -6 + g = 8.062257748 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + g = 8.062257748 + 6 Combine like terms: -6 + 6 = 0 0 + g = 8.062257748 + 6 g = 8.062257748 + 6 Combine like terms: 8.062257748 + 6 = 14.062257748 g = 14.062257748 Simplifying g = 14.062257748

Subproblem 2

g + -6 = -8.062257748 Simplifying g + -6 = -8.062257748 Reorder the terms: -6 + g = -8.062257748 Solving -6 + g = -8.062257748 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + g = -8.062257748 + 6 Combine like terms: -6 + 6 = 0 0 + g = -8.062257748 + 6 g = -8.062257748 + 6 Combine like terms: -8.062257748 + 6 = -2.062257748 g = -2.062257748 Simplifying g = -2.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. g = {14.062257748, -2.062257748}

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