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Simplifying 8h + h2 + 14 = 0 Reorder the terms: 14 + 8h + h2 = 0 Solving 14 + 8h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 8h + -14 + h2 = 0 + -14 Reorder the terms: 14 + -14 + 8h + h2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 8h + h2 = 0 + -14 8h + h2 = 0 + -14 Combine like terms: 0 + -14 = -14 8h + h2 = -14 The h term is 8h. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8h + 16 + h2 = -14 + 16 Reorder the terms: 16 + 8h + h2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + 8h + h2 = 2 Factor a perfect square on the left side: (h + 4)(h + 4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (h + 4) equal to 1.414213562 and -1.414213562.Subproblem 1
h + 4 = 1.414213562 Simplifying h + 4 = 1.414213562 Reorder the terms: 4 + h = 1.414213562 Solving 4 + h = 1.414213562 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + h = 1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + h = 1.414213562 + -4 h = 1.414213562 + -4 Combine like terms: 1.414213562 + -4 = -2.585786438 h = -2.585786438 Simplifying h = -2.585786438Subproblem 2
h + 4 = -1.414213562 Simplifying h + 4 = -1.414213562 Reorder the terms: 4 + h = -1.414213562 Solving 4 + h = -1.414213562 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + h = -1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + h = -1.414213562 + -4 h = -1.414213562 + -4 Combine like terms: -1.414213562 + -4 = -5.414213562 h = -5.414213562 Simplifying h = -5.414213562Solution
The solution to the problem is based on the solutions from the subproblems. h = {-2.585786438, -5.414213562}
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