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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 = 27.674794331 h = 27.674794331 Simplifying h = 27.674794331Subproblem 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 = 0.325205669 h = 0.325205669 Simplifying h = 0.325205669Solution
The solution to the problem is based on the solutions from the subproblems. h = {27.674794331, 0.325205669}
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