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Simplifying (8h2) + 24h + -563 = 0 Reorder the terms: -563 + 24h + (8h2) = 0 Solving -563 + 24h + (8h2) = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -70.375 + 3h + h2 = 0 Move the constant term to the right: Add '70.375' to each side of the equation. -70.375 + 3h + 70.375 + h2 = 0 + 70.375 Reorder the terms: -70.375 + 70.375 + 3h + h2 = 0 + 70.375 Combine like terms: -70.375 + 70.375 = 0.000 0.000 + 3h + h2 = 0 + 70.375 3h + h2 = 0 + 70.375 Combine like terms: 0 + 70.375 = 70.375 3h + h2 = 70.375 The h term is 3h. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3h + 2.25 + h2 = 70.375 + 2.25 Reorder the terms: 2.25 + 3h + h2 = 70.375 + 2.25 Combine like terms: 70.375 + 2.25 = 72.625 2.25 + 3h + h2 = 72.625 Factor a perfect square on the left side: ((h) + 1.5)((h) + 1.5) = 72.625 Calculate the square root of the right side: 8.522030275 Break this problem into two subproblems by setting ((h) + 1.5) equal to 8.522030275 and -8.522030275.Subproblem 1
(h) + 1.5 = 8.522030275 Simplifying (h) + 1.5 = 8.522030275 h + 1.5 = 8.522030275 Reorder the terms: 1.5 + h = 8.522030275 Solving 1.5 + h = 8.522030275 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = 8.522030275 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 8.522030275 + -1.5 h = 8.522030275 + -1.5 Combine like terms: 8.522030275 + -1.5 = 7.022030275 h = 7.022030275 Simplifying h = 7.022030275Subproblem 2
(h) + 1.5 = -8.522030275 Simplifying (h) + 1.5 = -8.522030275 h + 1.5 = -8.522030275 Reorder the terms: 1.5 + h = -8.522030275 Solving 1.5 + h = -8.522030275 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = -8.522030275 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -8.522030275 + -1.5 h = -8.522030275 + -1.5 Combine like terms: -8.522030275 + -1.5 = -10.022030275 h = -10.022030275 Simplifying h = -10.022030275Solution
The solution to the problem is based on the solutions from the subproblems. h = {7.022030275, -10.022030275}
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