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Simplifying -1g2 + 1 = -5g2 + 4g Reorder the terms: 1 + -1g2 = -5g2 + 4g Reorder the terms: 1 + -1g2 = 4g + -5g2 Solving 1 + -1g2 = 4g + -5g2 Solving for variable 'g'. Reorder the terms: 1 + -4g + -1g2 + 5g2 = 4g + -5g2 + -4g + 5g2 Combine like terms: -1g2 + 5g2 = 4g2 1 + -4g + 4g2 = 4g + -5g2 + -4g + 5g2 Reorder the terms: 1 + -4g + 4g2 = 4g + -4g + -5g2 + 5g2 Combine like terms: 4g + -4g = 0 1 + -4g + 4g2 = 0 + -5g2 + 5g2 1 + -4g + 4g2 = -5g2 + 5g2 Combine like terms: -5g2 + 5g2 = 0 1 + -4g + 4g2 = 0 Factor a trinomial. (1 + -2g)(1 + -2g) = 0Subproblem 1
Set the factor '(1 + -2g)' equal to zero and attempt to solve: Simplifying 1 + -2g = 0 Solving 1 + -2g = 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 + -2g = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2g = 0 + -1 -2g = 0 + -1 Combine like terms: 0 + -1 = -1 -2g = -1 Divide each side by '-2'. g = 0.5 Simplifying g = 0.5Subproblem 2
Set the factor '(1 + -2g)' equal to zero and attempt to solve: Simplifying 1 + -2g = 0 Solving 1 + -2g = 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 + -2g = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2g = 0 + -1 -2g = 0 + -1 Combine like terms: 0 + -1 = -1 -2g = -1 Divide each side by '-2'. g = 0.5 Simplifying g = 0.5Solution
g = {0.5, 0.5}
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