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Simplifying -3g2 + -72g + 144 = 0 Reorder the terms: 144 + -72g + -3g2 = 0 Solving 144 + -72g + -3g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '3'. 3(48 + -24g + -1g2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(48 + -24g + -1g2)' equal to zero and attempt to solve: Simplifying 48 + -24g + -1g2 = 0 Solving 48 + -24g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 24g + g2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 24g + 48 + g2 = 0 + 48 Reorder the terms: -48 + 48 + 24g + g2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 24g + g2 = 0 + 48 24g + g2 = 0 + 48 Combine like terms: 0 + 48 = 48 24g + g2 = 48 The g term is 24g. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24g + 144 + g2 = 48 + 144 Reorder the terms: 144 + 24g + g2 = 48 + 144 Combine like terms: 48 + 144 = 192 144 + 24g + g2 = 192 Factor a perfect square on the left side: (g + 12)(g + 12) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (g + 12) equal to 13.856406461 and -13.856406461.Subproblem 1
g + 12 = 13.856406461 Simplifying g + 12 = 13.856406461 Reorder the terms: 12 + g = 13.856406461 Solving 12 + g = 13.856406461 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + g = 13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + g = 13.856406461 + -12 g = 13.856406461 + -12 Combine like terms: 13.856406461 + -12 = 1.856406461 g = 1.856406461 Simplifying g = 1.856406461Subproblem 2
g + 12 = -13.856406461 Simplifying g + 12 = -13.856406461 Reorder the terms: 12 + g = -13.856406461 Solving 12 + g = -13.856406461 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + g = -13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + g = -13.856406461 + -12 g = -13.856406461 + -12 Combine like terms: -13.856406461 + -12 = -25.856406461 g = -25.856406461 Simplifying g = -25.856406461Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.856406461, -25.856406461}Solution
g = {1.856406461, -25.856406461}
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