g^2+6g-11=0

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Solution for g^2+6g-11=0 equation:


Simplifying
g2 + 6g + -11 = 0

Reorder the terms:
-11 + 6g + g2 = 0

Solving
-11 + 6g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 6g + 11 + g2 = 0 + 11

Reorder the terms:
-11 + 11 + 6g + g2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 6g + g2 = 0 + 11
6g + g2 = 0 + 11

Combine like terms: 0 + 11 = 11
6g + g2 = 11

The g term is 6g.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6g + 9 + g2 = 11 + 9

Reorder the terms:
9 + 6g + g2 = 11 + 9

Combine like terms: 11 + 9 = 20
9 + 6g + g2 = 20

Factor a perfect square on the left side:
(g + 3)(g + 3) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(g + 3) equal to 4.472135955 and -4.472135955.

Subproblem 1

g + 3 = 4.472135955 Simplifying g + 3 = 4.472135955 Reorder the terms: 3 + g = 4.472135955 Solving 3 + g = 4.472135955 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + g = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + g = 4.472135955 + -3 g = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 g = 1.472135955 Simplifying g = 1.472135955

Subproblem 2

g + 3 = -4.472135955 Simplifying g + 3 = -4.472135955 Reorder the terms: 3 + g = -4.472135955 Solving 3 + g = -4.472135955 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + g = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + g = -4.472135955 + -3 g = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 g = -7.472135955 Simplifying g = -7.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. g = {1.472135955, -7.472135955}

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