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Simplifying 64G2 + -192GH + 144H2 = 0 Reorder the terms: -192GH + 64G2 + 144H2 = 0 Solving -192GH + 64G2 + 144H2 = 0 Solving for variable 'G'. Factor out the Greatest Common Factor (GCF), '16'. 16(-12GH + 4G2 + 9H2) = 0 Factor a trinomial. 16((2G + -3H)(2G + -3H)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2G + -3H)' equal to zero and attempt to solve: Simplifying 2G + -3H = 0 Solving 2G + -3H = 0 Move all terms containing G to the left, all other terms to the right. Add '3H' to each side of the equation. 2G + -3H + 3H = 0 + 3H Combine like terms: -3H + 3H = 0 2G + 0 = 0 + 3H 2G = 0 + 3H Remove the zero: 2G = 3H Divide each side by '2'. G = 1.5H Simplifying G = 1.5HSubproblem 2
Set the factor '(2G + -3H)' equal to zero and attempt to solve: Simplifying 2G + -3H = 0 Solving 2G + -3H = 0 Move all terms containing G to the left, all other terms to the right. Add '3H' to each side of the equation. 2G + -3H + 3H = 0 + 3H Combine like terms: -3H + 3H = 0 2G + 0 = 0 + 3H 2G = 0 + 3H Remove the zero: 2G = 3H Divide each side by '2'. G = 1.5H Simplifying G = 1.5HSolution
G = {1.5H, 1.5H}
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