4-4g+g^2=10

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Solution for 4-4g+g^2=10 equation:


Simplifying
4 + -4g + g2 = 10

Solving
4 + -4g + g2 = 10

Solving for variable 'g'.

Reorder the terms:
4 + -10 + -4g + g2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + -4g + g2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + -4g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4g + 6 + g2 = 0 + 6

Reorder the terms:
-6 + 6 + -4g + g2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4g + g2 = 0 + 6
-4g + g2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4g + g2 = 6

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 = 6 + 4

Reorder the terms:
4 + -4g + g2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + -4g + g2 = 10

Factor a perfect square on the left side:
(g + -2)(g + -2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(g + -2) equal to 3.16227766 and -3.16227766.

Subproblem 1

g + -2 = 3.16227766 Simplifying g + -2 = 3.16227766 Reorder the terms: -2 + g = 3.16227766 Solving -2 + g = 3.16227766 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 = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + g = 3.16227766 + 2 g = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 g = 5.16227766 Simplifying g = 5.16227766

Subproblem 2

g + -2 = -3.16227766 Simplifying g + -2 = -3.16227766 Reorder the terms: -2 + g = -3.16227766 Solving -2 + g = -3.16227766 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 = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + g = -3.16227766 + 2 g = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 g = -1.16227766 Simplifying g = -1.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. g = {5.16227766, -1.16227766}

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