g^2-h^2+gh=

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Solution for g^2-h^2+gh= equation:


Simplifying
g2 + -1h2 + gh = 0

Reorder the terms:
gh + g2 + -1h2 = 0

Solving
gh + g2 + -1h2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add 'h2' to each side of the equation.
gh + g2 + -1h2 + h2 = 0 + h2

Combine like terms: -1h2 + h2 = 0
gh + g2 + 0 = 0 + h2
gh + g2 = 0 + h2
Remove the zero:
gh + g2 = h2

The g term is gh.  Take half its coefficient (0.5h).
Square it (0.25h2) and add it to both sides.

Add '0.25h2' to each side of the equation.
gh + g2 + 0.25h2 = h2 + 0.25h2

Combine like terms: h2 + 0.25h2 = 1.25h2
gh + g2 + 0.25h2 = 1.25h2

Factor a perfect square on the left side:
(g + 0.5h)(g + 0.5h) = 1.25h2

Calculate the square root of the right side: 1.118033989h

Break this problem into two subproblems by setting 
(g + 0.5h) equal to 1.118033989h and -1.118033989h.


Subproblem 1
g + 0.5h = 1.118033989h

Simplifying
g + 0.5h = 1.118033989h

Solving
g + 0.5h = 1.118033989h

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '-0.5h' to each side of the equation.
g + 0.5h + -0.5h = 1.118033989h + -0.5h

Combine like terms: 0.5h + -0.5h = 0.0
g + 0.0 = 1.118033989h + -0.5h
g = 1.118033989h + -0.5h

Combine like terms: 1.118033989h + -0.5h = 0.618033989h
g = 0.618033989h

Simplifying
g = 0.618033989h


Subproblem 2
g + 0.5h = -1.118033989h

Simplifying
g + 0.5h = -1.118033989h

Solving
g + 0.5h = -1.118033989h

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '-0.5h' to each side of the equation.
g + 0.5h + -0.5h = -1.118033989h + -0.5h

Combine like terms: 0.5h + -0.5h = 0.0
g + 0.0 = -1.118033989h + -0.5h
g = -1.118033989h + -0.5h

Combine like terms: -1.118033989h + -0.5h = -1.618033989h
g = -1.618033989h

Simplifying
g = -1.618033989h


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.618033989h, -1.618033989h}

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