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Simplifying h2 + -39h + -234 = 0 Reorder the terms: -234 + -39h + h2 = 0 Solving -234 + -39h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + -39h + 234 + h2 = 0 + 234 Reorder the terms: -234 + 234 + -39h + h2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + -39h + h2 = 0 + 234 -39h + h2 = 0 + 234 Combine like terms: 0 + 234 = 234 -39h + h2 = 234 The h term is -39h. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39h + 380.25 + h2 = 234 + 380.25 Reorder the terms: 380.25 + -39h + h2 = 234 + 380.25 Combine like terms: 234 + 380.25 = 614.25 380.25 + -39h + h2 = 614.25 Factor a perfect square on the left side: (h + -19.5)(h + -19.5) = 614.25 Calculate the square root of the right side: 24.784067463 Break this problem into two subproblems by setting (h + -19.5) equal to 24.784067463 and -24.784067463.Subproblem 1
h + -19.5 = 24.784067463 Simplifying h + -19.5 = 24.784067463 Reorder the terms: -19.5 + h = 24.784067463 Solving -19.5 + h = 24.784067463 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + h = 24.784067463 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + h = 24.784067463 + 19.5 h = 24.784067463 + 19.5 Combine like terms: 24.784067463 + 19.5 = 44.284067463 h = 44.284067463 Simplifying h = 44.284067463Subproblem 2
h + -19.5 = -24.784067463 Simplifying h + -19.5 = -24.784067463 Reorder the terms: -19.5 + h = -24.784067463 Solving -19.5 + h = -24.784067463 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + h = -24.784067463 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + h = -24.784067463 + 19.5 h = -24.784067463 + 19.5 Combine like terms: -24.784067463 + 19.5 = -5.284067463 h = -5.284067463 Simplifying h = -5.284067463Solution
The solution to the problem is based on the solutions from the subproblems. h = {44.284067463, -5.284067463}
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