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Simplifying h2 + 8h + -17 = 0 Reorder the terms: -17 + 8h + h2 = 0 Solving -17 + 8h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 8h + 17 + h2 = 0 + 17 Reorder the terms: -17 + 17 + 8h + h2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 8h + h2 = 0 + 17 8h + h2 = 0 + 17 Combine like terms: 0 + 17 = 17 8h + h2 = 17 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 = 17 + 16 Reorder the terms: 16 + 8h + h2 = 17 + 16 Combine like terms: 17 + 16 = 33 16 + 8h + h2 = 33 Factor a perfect square on the left side: (h + 4)(h + 4) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (h + 4) equal to 5.744562647 and -5.744562647.Subproblem 1
h + 4 = 5.744562647 Simplifying h + 4 = 5.744562647 Reorder the terms: 4 + h = 5.744562647 Solving 4 + h = 5.744562647 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 = 5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + h = 5.744562647 + -4 h = 5.744562647 + -4 Combine like terms: 5.744562647 + -4 = 1.744562647 h = 1.744562647 Simplifying h = 1.744562647Subproblem 2
h + 4 = -5.744562647 Simplifying h + 4 = -5.744562647 Reorder the terms: 4 + h = -5.744562647 Solving 4 + h = -5.744562647 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 = -5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + h = -5.744562647 + -4 h = -5.744562647 + -4 Combine like terms: -5.744562647 + -4 = -9.744562647 h = -9.744562647 Simplifying h = -9.744562647Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.744562647, -9.744562647}
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