g^2-4g-11=0

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Solution for g^2-4g-11=0 equation:


Simplifying
g2 + -4g + -11 = 0

Reorder the terms:
-11 + -4g + g2 = 0

Solving
-11 + -4g + 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 + -4g + 11 + g2 = 0 + 11

Reorder the terms:
-11 + 11 + -4g + g2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4g + g2 = 0 + 11
-4g + g2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4g + g2 = 11

The g term is -4g.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4g + 4 + g2 = 11 + 4

Reorder the terms:
4 + -4g + g2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + -4g + g2 = 15

Factor a perfect square on the left side:
(g + -2)(g + -2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(g + -2) equal to 3.872983346 and -3.872983346.

Subproblem 1

g + -2 = 3.872983346 Simplifying g + -2 = 3.872983346 Reorder the terms: -2 + g = 3.872983346 Solving -2 + g = 3.872983346 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = 3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + g = 3.872983346 + 2 g = 3.872983346 + 2 Combine like terms: 3.872983346 + 2 = 5.872983346 g = 5.872983346 Simplifying g = 5.872983346

Subproblem 2

g + -2 = -3.872983346 Simplifying g + -2 = -3.872983346 Reorder the terms: -2 + g = -3.872983346 Solving -2 + g = -3.872983346 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = -3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + g = -3.872983346 + 2 g = -3.872983346 + 2 Combine like terms: -3.872983346 + 2 = -1.872983346 g = -1.872983346 Simplifying g = -1.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. g = {5.872983346, -1.872983346}

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