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Simplifying h2 + 13h + -15 = 0 Reorder the terms: -15 + 13h + h2 = 0 Solving -15 + 13h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 13h + 15 + h2 = 0 + 15 Reorder the terms: -15 + 15 + 13h + h2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 13h + h2 = 0 + 15 13h + h2 = 0 + 15 Combine like terms: 0 + 15 = 15 13h + h2 = 15 The h term is 13h. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13h + 42.25 + h2 = 15 + 42.25 Reorder the terms: 42.25 + 13h + h2 = 15 + 42.25 Combine like terms: 15 + 42.25 = 57.25 42.25 + 13h + h2 = 57.25 Factor a perfect square on the left side: (h + 6.5)(h + 6.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (h + 6.5) equal to 7.566372975 and -7.566372975.Subproblem 1
h + 6.5 = 7.566372975 Simplifying h + 6.5 = 7.566372975 Reorder the terms: 6.5 + h = 7.566372975 Solving 6.5 + h = 7.566372975 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + h = 7.566372975 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + h = 7.566372975 + -6.5 h = 7.566372975 + -6.5 Combine like terms: 7.566372975 + -6.5 = 1.066372975 h = 1.066372975 Simplifying h = 1.066372975Subproblem 2
h + 6.5 = -7.566372975 Simplifying h + 6.5 = -7.566372975 Reorder the terms: 6.5 + h = -7.566372975 Solving 6.5 + h = -7.566372975 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + h = -7.566372975 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + h = -7.566372975 + -6.5 h = -7.566372975 + -6.5 Combine like terms: -7.566372975 + -6.5 = -14.066372975 h = -14.066372975 Simplifying h = -14.066372975Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.066372975, -14.066372975}
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