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Simplifying 6g2 + 18g = 54 Reorder the terms: 18g + 6g2 = 54 Solving 18g + 6g2 = 54 Solving for variable 'g'. Reorder the terms: -54 + 18g + 6g2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 18g + 6g2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + 3g + g2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + 3g + g2)' equal to zero and attempt to solve: Simplifying -9 + 3g + g2 = 0 Solving -9 + 3g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 3g + 9 + g2 = 0 + 9 Reorder the terms: -9 + 9 + 3g + g2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3g + g2 = 0 + 9 3g + g2 = 0 + 9 Combine like terms: 0 + 9 = 9 3g + g2 = 9 The g term is 3g. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3g + 2.25 + g2 = 9 + 2.25 Reorder the terms: 2.25 + 3g + g2 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + 3g + g2 = 11.25 Factor a perfect square on the left side: (g + 1.5)(g + 1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (g + 1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
g + 1.5 = 3.354101966 Simplifying g + 1.5 = 3.354101966 Reorder the terms: 1.5 + g = 3.354101966 Solving 1.5 + g = 3.354101966 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + g = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + g = 3.354101966 + -1.5 g = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 g = 1.854101966 Simplifying g = 1.854101966Subproblem 2
g + 1.5 = -3.354101966 Simplifying g + 1.5 = -3.354101966 Reorder the terms: 1.5 + g = -3.354101966 Solving 1.5 + g = -3.354101966 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + g = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + g = -3.354101966 + -1.5 g = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 g = -4.854101966 Simplifying g = -4.854101966Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.854101966, -4.854101966}Solution
g = {1.854101966, -4.854101966}
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