g^2+22g-3=0

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Solution for g^2+22g-3=0 equation:


Simplifying
g2 + 22g + -3 = 0

Reorder the terms:
-3 + 22g + g2 = 0

Solving
-3 + 22g + 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 + 22g + 3 + g2 = 0 + 3

Reorder the terms:
-3 + 3 + 22g + g2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 22g + g2 = 0 + 3
22g + g2 = 0 + 3

Combine like terms: 0 + 3 = 3
22g + g2 = 3

The g term is 22g.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22g + 121 + g2 = 3 + 121

Reorder the terms:
121 + 22g + g2 = 3 + 121

Combine like terms: 3 + 121 = 124
121 + 22g + g2 = 124

Factor a perfect square on the left side:
(g + 11)(g + 11) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(g + 11) equal to 11.135528726 and -11.135528726.

Subproblem 1

g + 11 = 11.135528726 Simplifying g + 11 = 11.135528726 Reorder the terms: 11 + g = 11.135528726 Solving 11 + g = 11.135528726 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + g = 11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + g = 11.135528726 + -11 g = 11.135528726 + -11 Combine like terms: 11.135528726 + -11 = 0.135528726 g = 0.135528726 Simplifying g = 0.135528726

Subproblem 2

g + 11 = -11.135528726 Simplifying g + 11 = -11.135528726 Reorder the terms: 11 + g = -11.135528726 Solving 11 + g = -11.135528726 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + g = -11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + g = -11.135528726 + -11 g = -11.135528726 + -11 Combine like terms: -11.135528726 + -11 = -22.135528726 g = -22.135528726 Simplifying g = -22.135528726

Solution

The solution to the problem is based on the solutions from the subproblems. g = {0.135528726, -22.135528726}

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