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Simplifying -3h2 + -60h = 117 Reorder the terms: -60h + -3h2 = 117 Solving -60h + -3h2 = 117 Solving for variable 'h'. Reorder the terms: -117 + -60h + -3h2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + -60h + -3h2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(39 + 20h + h2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(39 + 20h + h2)' equal to zero and attempt to solve: Simplifying 39 + 20h + h2 = 0 Solving 39 + 20h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 20h + -39 + h2 = 0 + -39 Reorder the terms: 39 + -39 + 20h + h2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 20h + h2 = 0 + -39 20h + h2 = 0 + -39 Combine like terms: 0 + -39 = -39 20h + h2 = -39 The h term is 20h. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20h + 100 + h2 = -39 + 100 Reorder the terms: 100 + 20h + h2 = -39 + 100 Combine like terms: -39 + 100 = 61 100 + 20h + h2 = 61 Factor a perfect square on the left side: (h + 10)(h + 10) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (h + 10) equal to 7.810249676 and -7.810249676.Subproblem 1
h + 10 = 7.810249676 Simplifying h + 10 = 7.810249676 Reorder the terms: 10 + h = 7.810249676 Solving 10 + h = 7.810249676 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = 7.810249676 + -10 Combine like terms: 10 + -10 = 0 0 + h = 7.810249676 + -10 h = 7.810249676 + -10 Combine like terms: 7.810249676 + -10 = -2.189750324 h = -2.189750324 Simplifying h = -2.189750324Subproblem 2
h + 10 = -7.810249676 Simplifying h + 10 = -7.810249676 Reorder the terms: 10 + h = -7.810249676 Solving 10 + h = -7.810249676 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = -7.810249676 + -10 Combine like terms: 10 + -10 = 0 0 + h = -7.810249676 + -10 h = -7.810249676 + -10 Combine like terms: -7.810249676 + -10 = -17.810249676 h = -17.810249676 Simplifying h = -17.810249676Solution
The solution to the problem is based on the solutions from the subproblems. h = {-2.189750324, -17.810249676}Solution
h = {-2.189750324, -17.810249676}
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