g^2+12g-47=0

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Solution for g^2+12g-47=0 equation:


Simplifying
g2 + 12g + -47 = 0

Reorder the terms:
-47 + 12g + g2 = 0

Solving
-47 + 12g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 12g + 47 + g2 = 0 + 47

Reorder the terms:
-47 + 47 + 12g + g2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 12g + g2 = 0 + 47
12g + g2 = 0 + 47

Combine like terms: 0 + 47 = 47
12g + g2 = 47

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 = 47 + 36

Reorder the terms:
36 + 12g + g2 = 47 + 36

Combine like terms: 47 + 36 = 83
36 + 12g + g2 = 83

Factor a perfect square on the left side:
(g + 6)(g + 6) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(g + 6) equal to 9.110433579 and -9.110433579.

Subproblem 1

g + 6 = 9.110433579 Simplifying g + 6 = 9.110433579 Reorder the terms: 6 + g = 9.110433579 Solving 6 + g = 9.110433579 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 = 9.110433579 + -6 Combine like terms: 6 + -6 = 0 0 + g = 9.110433579 + -6 g = 9.110433579 + -6 Combine like terms: 9.110433579 + -6 = 3.110433579 g = 3.110433579 Simplifying g = 3.110433579

Subproblem 2

g + 6 = -9.110433579 Simplifying g + 6 = -9.110433579 Reorder the terms: 6 + g = -9.110433579 Solving 6 + g = -9.110433579 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 = -9.110433579 + -6 Combine like terms: 6 + -6 = 0 0 + g = -9.110433579 + -6 g = -9.110433579 + -6 Combine like terms: -9.110433579 + -6 = -15.110433579 g = -15.110433579 Simplifying g = -15.110433579

Solution

The solution to the problem is based on the solutions from the subproblems. g = {3.110433579, -15.110433579}

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