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Simplifying 11h2 + 40h + 32 = 0 Reorder the terms: 32 + 40h + 11h2 = 0 Solving 32 + 40h + 11h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 2.909090909 + 3.636363636h + h2 = 0 Move the constant term to the right: Add '-2.909090909' to each side of the equation. 2.909090909 + 3.636363636h + -2.909090909 + h2 = 0 + -2.909090909 Reorder the terms: 2.909090909 + -2.909090909 + 3.636363636h + h2 = 0 + -2.909090909 Combine like terms: 2.909090909 + -2.909090909 = 0.000000000 0.000000000 + 3.636363636h + h2 = 0 + -2.909090909 3.636363636h + h2 = 0 + -2.909090909 Combine like terms: 0 + -2.909090909 = -2.909090909 3.636363636h + h2 = -2.909090909 The h term is 3.636363636h. Take half its coefficient (1.818181818). Square it (3.305785123) and add it to both sides. Add '3.305785123' to each side of the equation. 3.636363636h + 3.305785123 + h2 = -2.909090909 + 3.305785123 Reorder the terms: 3.305785123 + 3.636363636h + h2 = -2.909090909 + 3.305785123 Combine like terms: -2.909090909 + 3.305785123 = 0.396694214 3.305785123 + 3.636363636h + h2 = 0.396694214 Factor a perfect square on the left side: (h + 1.818181818)(h + 1.818181818) = 0.396694214 Calculate the square root of the right side: 0.629836657 Break this problem into two subproblems by setting (h + 1.818181818) equal to 0.629836657 and -0.629836657.Subproblem 1
h + 1.818181818 = 0.629836657 Simplifying h + 1.818181818 = 0.629836657 Reorder the terms: 1.818181818 + h = 0.629836657 Solving 1.818181818 + h = 0.629836657 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + h = 0.629836657 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + h = 0.629836657 + -1.818181818 h = 0.629836657 + -1.818181818 Combine like terms: 0.629836657 + -1.818181818 = -1.188345161 h = -1.188345161 Simplifying h = -1.188345161Subproblem 2
h + 1.818181818 = -0.629836657 Simplifying h + 1.818181818 = -0.629836657 Reorder the terms: 1.818181818 + h = -0.629836657 Solving 1.818181818 + h = -0.629836657 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + h = -0.629836657 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + h = -0.629836657 + -1.818181818 h = -0.629836657 + -1.818181818 Combine like terms: -0.629836657 + -1.818181818 = -2.448018475 h = -2.448018475 Simplifying h = -2.448018475Solution
The solution to the problem is based on the solutions from the subproblems. h = {-1.188345161, -2.448018475}
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