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Simplifying -2g2 + 56g = 58 Reorder the terms: 56g + -2g2 = 58 Solving 56g + -2g2 = 58 Solving for variable 'g'. Reorder the terms: -58 + 56g + -2g2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 56g + -2g2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + 28g + -1g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + 28g + -1g2)' equal to zero and attempt to solve: Simplifying -29 + 28g + -1g2 = 0 Solving -29 + 28g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 29 + -28g + g2 = 0 Move the constant term to the right: Add '-29' to each side of the equation. 29 + -28g + -29 + g2 = 0 + -29 Reorder the terms: 29 + -29 + -28g + g2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -28g + g2 = 0 + -29 -28g + g2 = 0 + -29 Combine like terms: 0 + -29 = -29 -28g + g2 = -29 The g term is -28g. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28g + 196 + g2 = -29 + 196 Reorder the terms: 196 + -28g + g2 = -29 + 196 Combine like terms: -29 + 196 = 167 196 + -28g + g2 = 167 Factor a perfect square on the left side: (g + -14)(g + -14) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (g + -14) equal to 12.922847983 and -12.922847983.Subproblem 1
g + -14 = 12.922847983 Simplifying g + -14 = 12.922847983 Reorder the terms: -14 + g = 12.922847983 Solving -14 + g = 12.922847983 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + g = 12.922847983 + 14 Combine like terms: -14 + 14 = 0 0 + g = 12.922847983 + 14 g = 12.922847983 + 14 Combine like terms: 12.922847983 + 14 = 26.922847983 g = 26.922847983 Simplifying g = 26.922847983Subproblem 2
g + -14 = -12.922847983 Simplifying g + -14 = -12.922847983 Reorder the terms: -14 + g = -12.922847983 Solving -14 + g = -12.922847983 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + g = -12.922847983 + 14 Combine like terms: -14 + 14 = 0 0 + g = -12.922847983 + 14 g = -12.922847983 + 14 Combine like terms: -12.922847983 + 14 = 1.077152017 g = 1.077152017 Simplifying g = 1.077152017Solution
The solution to the problem is based on the solutions from the subproblems. g = {26.922847983, 1.077152017}Solution
g = {26.922847983, 1.077152017}
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