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Simplifying 0 = g2 + -120g + 28 Reorder the terms: 0 = 28 + -120g + g2 Solving 0 = 28 + -120g + g2 Solving for variable 'g'. Combine like terms: 0 + -28 = -28 -28 + 120g + -1g2 = 28 + -120g + g2 + -28 + 120g + -1g2 Reorder the terms: -28 + 120g + -1g2 = 28 + -28 + -120g + 120g + g2 + -1g2 Combine like terms: 28 + -28 = 0 -28 + 120g + -1g2 = 0 + -120g + 120g + g2 + -1g2 -28 + 120g + -1g2 = -120g + 120g + g2 + -1g2 Combine like terms: -120g + 120g = 0 -28 + 120g + -1g2 = 0 + g2 + -1g2 -28 + 120g + -1g2 = g2 + -1g2 Combine like terms: g2 + -1g2 = 0 -28 + 120g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 28 + -120g + g2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -120g + -28 + g2 = 0 + -28 Reorder the terms: 28 + -28 + -120g + g2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -120g + g2 = 0 + -28 -120g + g2 = 0 + -28 Combine like terms: 0 + -28 = -28 -120g + g2 = -28 The g term is -120g. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120g + 3600 + g2 = -28 + 3600 Reorder the terms: 3600 + -120g + g2 = -28 + 3600 Combine like terms: -28 + 3600 = 3572 3600 + -120g + g2 = 3572 Factor a perfect square on the left side: (g + -60)(g + -60) = 3572 Calculate the square root of the right side: 59.76621119 Break this problem into two subproblems by setting (g + -60) equal to 59.76621119 and -59.76621119.Subproblem 1
g + -60 = 59.76621119 Simplifying g + -60 = 59.76621119 Reorder the terms: -60 + g = 59.76621119 Solving -60 + g = 59.76621119 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + g = 59.76621119 + 60 Combine like terms: -60 + 60 = 0 0 + g = 59.76621119 + 60 g = 59.76621119 + 60 Combine like terms: 59.76621119 + 60 = 119.76621119 g = 119.76621119 Simplifying g = 119.76621119Subproblem 2
g + -60 = -59.76621119 Simplifying g + -60 = -59.76621119 Reorder the terms: -60 + g = -59.76621119 Solving -60 + g = -59.76621119 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + g = -59.76621119 + 60 Combine like terms: -60 + 60 = 0 0 + g = -59.76621119 + 60 g = -59.76621119 + 60 Combine like terms: -59.76621119 + 60 = 0.23378881 g = 0.23378881 Simplifying g = 0.23378881Solution
The solution to the problem is based on the solutions from the subproblems. g = {119.76621119, 0.23378881}
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