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Simplifying g2 + -28g = -9 Reorder the terms: -28g + g2 = -9 Solving -28g + g2 = -9 Solving for variable 'g'. Reorder the terms: 9 + -28g + g2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -28g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -28g + -9 + g2 = 0 + -9 Reorder the terms: 9 + -9 + -28g + g2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -28g + g2 = 0 + -9 -28g + g2 = 0 + -9 Combine like terms: 0 + -9 = -9 -28g + g2 = -9 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 = -9 + 196 Reorder the terms: 196 + -28g + g2 = -9 + 196 Combine like terms: -9 + 196 = 187 196 + -28g + g2 = 187 Factor a perfect square on the left side: (g + -14)(g + -14) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (g + -14) equal to 13.674794331 and -13.674794331.Subproblem 1
g + -14 = 13.674794331 Simplifying g + -14 = 13.674794331 Reorder the terms: -14 + g = 13.674794331 Solving -14 + g = 13.674794331 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 = 13.674794331 + 14 Combine like terms: -14 + 14 = 0 0 + g = 13.674794331 + 14 g = 13.674794331 + 14 Combine like terms: 13.674794331 + 14 = 27.674794331 g = 27.674794331 Simplifying g = 27.674794331Subproblem 2
g + -14 = -13.674794331 Simplifying g + -14 = -13.674794331 Reorder the terms: -14 + g = -13.674794331 Solving -14 + g = -13.674794331 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 = -13.674794331 + 14 Combine like terms: -14 + 14 = 0 0 + g = -13.674794331 + 14 g = -13.674794331 + 14 Combine like terms: -13.674794331 + 14 = 0.325205669 g = 0.325205669 Simplifying g = 0.325205669Solution
The solution to the problem is based on the solutions from the subproblems. g = {27.674794331, 0.325205669}
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