g^2+20g-36=0

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Solution for g^2+20g-36=0 equation:


Simplifying
g2 + 20g + -36 = 0

Reorder the terms:
-36 + 20g + g2 = 0

Solving
-36 + 20g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 20g + 36 + g2 = 0 + 36

Reorder the terms:
-36 + 36 + 20g + g2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 20g + g2 = 0 + 36
20g + g2 = 0 + 36

Combine like terms: 0 + 36 = 36
20g + g2 = 36

The g term is 20g.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20g + 100 + g2 = 36 + 100

Reorder the terms:
100 + 20g + g2 = 36 + 100

Combine like terms: 36 + 100 = 136
100 + 20g + g2 = 136

Factor a perfect square on the left side:
(g + 10)(g + 10) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(g + 10) equal to 11.66190379 and -11.66190379.

Subproblem 1

g + 10 = 11.66190379 Simplifying g + 10 = 11.66190379 Reorder the terms: 10 + g = 11.66190379 Solving 10 + g = 11.66190379 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + g = 11.66190379 + -10 Combine like terms: 10 + -10 = 0 0 + g = 11.66190379 + -10 g = 11.66190379 + -10 Combine like terms: 11.66190379 + -10 = 1.66190379 g = 1.66190379 Simplifying g = 1.66190379

Subproblem 2

g + 10 = -11.66190379 Simplifying g + 10 = -11.66190379 Reorder the terms: 10 + g = -11.66190379 Solving 10 + g = -11.66190379 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + g = -11.66190379 + -10 Combine like terms: 10 + -10 = 0 0 + g = -11.66190379 + -10 g = -11.66190379 + -10 Combine like terms: -11.66190379 + -10 = -21.66190379 g = -21.66190379 Simplifying g = -21.66190379

Solution

The solution to the problem is based on the solutions from the subproblems. g = {1.66190379, -21.66190379}

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