g^2-6g-10=0

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Solution for g^2-6g-10=0 equation:


Simplifying
g2 + -6g + -10 = 0

Reorder the terms:
-10 + -6g + g2 = 0

Solving
-10 + -6g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -6g + 10 + g2 = 0 + 10

Reorder the terms:
-10 + 10 + -6g + g2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -6g + g2 = 0 + 10
-6g + g2 = 0 + 10

Combine like terms: 0 + 10 = 10
-6g + g2 = 10

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 = 10 + 9

Reorder the terms:
9 + -6g + g2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + -6g + g2 = 19

Factor a perfect square on the left side:
(g + -3)(g + -3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(g + -3) equal to 4.358898944 and -4.358898944.

Subproblem 1

g + -3 = 4.358898944 Simplifying g + -3 = 4.358898944 Reorder the terms: -3 + g = 4.358898944 Solving -3 + g = 4.358898944 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 = 4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + g = 4.358898944 + 3 g = 4.358898944 + 3 Combine like terms: 4.358898944 + 3 = 7.358898944 g = 7.358898944 Simplifying g = 7.358898944

Subproblem 2

g + -3 = -4.358898944 Simplifying g + -3 = -4.358898944 Reorder the terms: -3 + g = -4.358898944 Solving -3 + g = -4.358898944 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 = -4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + g = -4.358898944 + 3 g = -4.358898944 + 3 Combine like terms: -4.358898944 + 3 = -1.358898944 g = -1.358898944 Simplifying g = -1.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. g = {7.358898944, -1.358898944}

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