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Simplifying -4g2 + 40g + 116 = 0 Reorder the terms: 116 + 40g + -4g2 = 0 Solving 116 + 40g + -4g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '4'. 4(29 + 10g + -1g2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + 10g + -1g2)' equal to zero and attempt to solve: Simplifying 29 + 10g + -1g2 = 0 Solving 29 + 10g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + -10g + g2 = 0 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 = 12.348469228 g = 12.348469228 Simplifying g = 12.348469228Subproblem 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 = -2.348469228 g = -2.348469228 Simplifying g = -2.348469228Solution
The solution to the problem is based on the solutions from the subproblems. g = {12.348469228, -2.348469228}Solution
g = {12.348469228, -2.348469228}
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