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Simplifying h2 + 26h + -18 = 0 Reorder the terms: -18 + 26h + h2 = 0 Solving -18 + 26h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 26h + 18 + h2 = 0 + 18 Reorder the terms: -18 + 18 + 26h + h2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 26h + h2 = 0 + 18 26h + h2 = 0 + 18 Combine like terms: 0 + 18 = 18 26h + h2 = 18 The h term is 26h. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26h + 169 + h2 = 18 + 169 Reorder the terms: 169 + 26h + h2 = 18 + 169 Combine like terms: 18 + 169 = 187 169 + 26h + h2 = 187 Factor a perfect square on the left side: (h + 13)(h + 13) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (h + 13) equal to 13.674794331 and -13.674794331.Subproblem 1
h + 13 = 13.674794331 Simplifying h + 13 = 13.674794331 Reorder the terms: 13 + h = 13.674794331 Solving 13 + h = 13.674794331 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + h = 13.674794331 + -13 Combine like terms: 13 + -13 = 0 0 + h = 13.674794331 + -13 h = 13.674794331 + -13 Combine like terms: 13.674794331 + -13 = 0.674794331 h = 0.674794331 Simplifying h = 0.674794331Subproblem 2
h + 13 = -13.674794331 Simplifying h + 13 = -13.674794331 Reorder the terms: 13 + h = -13.674794331 Solving 13 + h = -13.674794331 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + h = -13.674794331 + -13 Combine like terms: 13 + -13 = 0 0 + h = -13.674794331 + -13 h = -13.674794331 + -13 Combine like terms: -13.674794331 + -13 = -26.674794331 h = -26.674794331 Simplifying h = -26.674794331Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.674794331, -26.674794331}
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