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Simplifying 3g2 + 30g = 87 Reorder the terms: 30g + 3g2 = 87 Solving 30g + 3g2 = 87 Solving for variable 'g'. Reorder the terms: -87 + 30g + 3g2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + 30g + 3g2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + 10g + g2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + 10g + g2)' equal to zero and attempt to solve: Simplifying -29 + 10g + g2 = 0 Solving -29 + 10g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 10g + 29 + g2 = 0 + 29 Reorder the terms: -29 + 29 + 10g + g2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 10g + g2 = 0 + 29 10g + g2 = 0 + 29 Combine like terms: 0 + 29 = 29 10g + g2 = 29 The g term is 10g. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10g + 25 + g2 = 29 + 25 Reorder the terms: 25 + 10g + g2 = 29 + 25 Combine like terms: 29 + 25 = 54 25 + 10g + g2 = 54 Factor a perfect square on the left side: (g + 5)(g + 5) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (g + 5) equal to 7.348469228 and -7.348469228.Subproblem 1
g + 5 = 7.348469228 Simplifying g + 5 = 7.348469228 Reorder the terms: 5 + g = 7.348469228 Solving 5 + g = 7.348469228 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + g = 7.348469228 + -5 Combine like terms: 5 + -5 = 0 0 + g = 7.348469228 + -5 g = 7.348469228 + -5 Combine like terms: 7.348469228 + -5 = 2.348469228 g = 2.348469228 Simplifying g = 2.348469228Subproblem 2
g + 5 = -7.348469228 Simplifying g + 5 = -7.348469228 Reorder the terms: 5 + g = -7.348469228 Solving 5 + g = -7.348469228 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + g = -7.348469228 + -5 Combine like terms: 5 + -5 = 0 0 + g = -7.348469228 + -5 g = -7.348469228 + -5 Combine like terms: -7.348469228 + -5 = -12.348469228 g = -12.348469228 Simplifying g = -12.348469228Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.348469228, -12.348469228}Solution
g = {2.348469228, -12.348469228}
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