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Simplifying (g2 + -2g + 4) + (2g2 + g + -8) = 0 Reorder the terms: (4 + -2g + g2) + (2g2 + g + -8) = 0 Remove parenthesis around (4 + -2g + g2) 4 + -2g + g2 + (2g2 + g + -8) = 0 Reorder the terms: 4 + -2g + g2 + (-8 + g + 2g2) = 0 Remove parenthesis around (-8 + g + 2g2) 4 + -2g + g2 + -8 + g + 2g2 = 0 Reorder the terms: 4 + -8 + -2g + g + g2 + 2g2 = 0 Combine like terms: 4 + -8 = -4 -4 + -2g + g + g2 + 2g2 = 0 Combine like terms: -2g + g = -1g -4 + -1g + g2 + 2g2 = 0 Combine like terms: g2 + 2g2 = 3g2 -4 + -1g + 3g2 = 0 Solving -4 + -1g + 3g2 = 0 Solving for variable 'g'. Factor a trinomial. (-1 + -1g)(4 + -3g) = 0Subproblem 1
Set the factor '(-1 + -1g)' equal to zero and attempt to solve: Simplifying -1 + -1g = 0 Solving -1 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1g = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1g = 0 + 1 -1g = 0 + 1 Combine like terms: 0 + 1 = 1 -1g = 1 Divide each side by '-1'. g = -1 Simplifying g = -1Subproblem 2
Set the factor '(4 + -3g)' equal to zero and attempt to solve: Simplifying 4 + -3g = 0 Solving 4 + -3g = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3g = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3g = 0 + -4 -3g = 0 + -4 Combine like terms: 0 + -4 = -4 -3g = -4 Divide each side by '-3'. g = 1.333333333 Simplifying g = 1.333333333Solution
g = {-1, 1.333333333}
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