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Simplifying h2 + 28h = -9 Reorder the terms: 28h + h2 = -9 Solving 28h + h2 = -9 Solving for variable 'h'. Reorder the terms: 9 + 28h + h2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 28h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 28h + -9 + h2 = 0 + -9 Reorder the terms: 9 + -9 + 28h + h2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 28h + h2 = 0 + -9 28h + h2 = 0 + -9 Combine like terms: 0 + -9 = -9 28h + h2 = -9 The h term is 28h. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28h + 196 + h2 = -9 + 196 Reorder the terms: 196 + 28h + h2 = -9 + 196 Combine like terms: -9 + 196 = 187 196 + 28h + h2 = 187 Factor a perfect square on the left side: (h + 14)(h + 14) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (h + 14) equal to 13.674794331 and -13.674794331.Subproblem 1
h + 14 = 13.674794331 Simplifying h + 14 = 13.674794331 Reorder the terms: 14 + h = 13.674794331 Solving 14 + h = 13.674794331 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + h = 13.674794331 + -14 Combine like terms: 14 + -14 = 0 0 + h = 13.674794331 + -14 h = 13.674794331 + -14 Combine like terms: 13.674794331 + -14 = -0.325205669 h = -0.325205669 Simplifying h = -0.325205669Subproblem 2
h + 14 = -13.674794331 Simplifying h + 14 = -13.674794331 Reorder the terms: 14 + h = -13.674794331 Solving 14 + h = -13.674794331 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + h = -13.674794331 + -14 Combine like terms: 14 + -14 = 0 0 + h = -13.674794331 + -14 h = -13.674794331 + -14 Combine like terms: -13.674794331 + -14 = -27.674794331 h = -27.674794331 Simplifying h = -27.674794331Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.325205669, -27.674794331}
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