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Simplifying 0 = 2(5g2 + -14g + 8) Reorder the terms: 0 = 2(8 + -14g + 5g2) 0 = (8 * 2 + -14g * 2 + 5g2 * 2) 0 = (16 + -28g + 10g2) Solving 0 = 16 + -28g + 10g2 Solving for variable 'g'. Combine like terms: 0 + -16 = -16 -16 + 28g + -10g2 = 16 + -28g + 10g2 + -16 + 28g + -10g2 Reorder the terms: -16 + 28g + -10g2 = 16 + -16 + -28g + 28g + 10g2 + -10g2 Combine like terms: 16 + -16 = 0 -16 + 28g + -10g2 = 0 + -28g + 28g + 10g2 + -10g2 -16 + 28g + -10g2 = -28g + 28g + 10g2 + -10g2 Combine like terms: -28g + 28g = 0 -16 + 28g + -10g2 = 0 + 10g2 + -10g2 -16 + 28g + -10g2 = 10g2 + -10g2 Combine like terms: 10g2 + -10g2 = 0 -16 + 28g + -10g2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 14g + -5g2) = 0 Factor a trinomial. 2((-2 + g)(4 + -5g)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + g)' equal to zero and attempt to solve: Simplifying -2 + g = 0 Solving -2 + g = 0 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 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + g = 0 + 2 g = 0 + 2 Combine like terms: 0 + 2 = 2 g = 2 Simplifying g = 2Subproblem 2
Set the factor '(4 + -5g)' equal to zero and attempt to solve: Simplifying 4 + -5g = 0 Solving 4 + -5g = 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 + -5g = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5g = 0 + -4 -5g = 0 + -4 Combine like terms: 0 + -4 = -4 -5g = -4 Divide each side by '-5'. g = 0.8 Simplifying g = 0.8Solution
g = {2, 0.8}
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