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Simplifying h2 + 11h + -36 = 0 Reorder the terms: -36 + 11h + h2 = 0 Solving -36 + 11h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 11h + 36 + h2 = 0 + 36 Reorder the terms: -36 + 36 + 11h + h2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 11h + h2 = 0 + 36 11h + h2 = 0 + 36 Combine like terms: 0 + 36 = 36 11h + h2 = 36 The h term is 11h. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11h + 30.25 + h2 = 36 + 30.25 Reorder the terms: 30.25 + 11h + h2 = 36 + 30.25 Combine like terms: 36 + 30.25 = 66.25 30.25 + 11h + h2 = 66.25 Factor a perfect square on the left side: (h + 5.5)(h + 5.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (h + 5.5) equal to 8.139410298 and -8.139410298.Subproblem 1
h + 5.5 = 8.139410298 Simplifying h + 5.5 = 8.139410298 Reorder the terms: 5.5 + h = 8.139410298 Solving 5.5 + h = 8.139410298 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + h = 8.139410298 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + h = 8.139410298 + -5.5 h = 8.139410298 + -5.5 Combine like terms: 8.139410298 + -5.5 = 2.639410298 h = 2.639410298 Simplifying h = 2.639410298Subproblem 2
h + 5.5 = -8.139410298 Simplifying h + 5.5 = -8.139410298 Reorder the terms: 5.5 + h = -8.139410298 Solving 5.5 + h = -8.139410298 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + h = -8.139410298 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + h = -8.139410298 + -5.5 h = -8.139410298 + -5.5 Combine like terms: -8.139410298 + -5.5 = -13.639410298 h = -13.639410298 Simplifying h = -13.639410298Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.639410298, -13.639410298}
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