g^2-10g+11=0

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Solution for g^2-10g+11=0 equation:


Simplifying
g2 + -10g + 11 = 0

Reorder the terms:
11 + -10g + g2 = 0

Solving
11 + -10g + 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 + -10g + -11 + g2 = 0 + -11

Reorder the terms:
11 + -11 + -10g + g2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10g + g2 = 0 + -11
-10g + g2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10g + g2 = -11

The g term is -10g.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10g + 25 + g2 = -11 + 25

Reorder the terms:
25 + -10g + g2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10g + g2 = 14

Factor a perfect square on the left side:
(g + -5)(g + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(g + -5) equal to 3.741657387 and -3.741657387.

Subproblem 1

g + -5 = 3.741657387 Simplifying g + -5 = 3.741657387 Reorder the terms: -5 + g = 3.741657387 Solving -5 + g = 3.741657387 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + g = 3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + g = 3.741657387 + 5 g = 3.741657387 + 5 Combine like terms: 3.741657387 + 5 = 8.741657387 g = 8.741657387 Simplifying g = 8.741657387

Subproblem 2

g + -5 = -3.741657387 Simplifying g + -5 = -3.741657387 Reorder the terms: -5 + g = -3.741657387 Solving -5 + g = -3.741657387 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + g = -3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + g = -3.741657387 + 5 g = -3.741657387 + 5 Combine like terms: -3.741657387 + 5 = 1.258342613 g = 1.258342613 Simplifying g = 1.258342613

Solution

The solution to the problem is based on the solutions from the subproblems. g = {8.741657387, 1.258342613}

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