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Simplifying 42g2 + -69g + 20 = 7g2 + -8 Reorder the terms: 20 + -69g + 42g2 = 7g2 + -8 Reorder the terms: 20 + -69g + 42g2 = -8 + 7g2 Solving 20 + -69g + 42g2 = -8 + 7g2 Solving for variable 'g'. Reorder the terms: 20 + 8 + -69g + 42g2 + -7g2 = -8 + 7g2 + 8 + -7g2 Combine like terms: 20 + 8 = 28 28 + -69g + 42g2 + -7g2 = -8 + 7g2 + 8 + -7g2 Combine like terms: 42g2 + -7g2 = 35g2 28 + -69g + 35g2 = -8 + 7g2 + 8 + -7g2 Reorder the terms: 28 + -69g + 35g2 = -8 + 8 + 7g2 + -7g2 Combine like terms: -8 + 8 = 0 28 + -69g + 35g2 = 0 + 7g2 + -7g2 28 + -69g + 35g2 = 7g2 + -7g2 Combine like terms: 7g2 + -7g2 = 0 28 + -69g + 35g2 = 0 Factor a trinomial. (4 + -7g)(7 + -5g) = 0Subproblem 1
Set the factor '(4 + -7g)' equal to zero and attempt to solve: Simplifying 4 + -7g = 0 Solving 4 + -7g = 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 + -7g = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7g = 0 + -4 -7g = 0 + -4 Combine like terms: 0 + -4 = -4 -7g = -4 Divide each side by '-7'. g = 0.5714285714 Simplifying g = 0.5714285714Subproblem 2
Set the factor '(7 + -5g)' equal to zero and attempt to solve: Simplifying 7 + -5g = 0 Solving 7 + -5g = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5g = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5g = 0 + -7 -5g = 0 + -7 Combine like terms: 0 + -7 = -7 -5g = -7 Divide each side by '-5'. g = 1.4 Simplifying g = 1.4Solution
g = {0.5714285714, 1.4}
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