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Simplifying (2h2 + 25h + -30) = 0 Reorder the terms: (-30 + 25h + 2h2) = 0 Remove parenthesis around (-30 + 25h + 2h2) -30 + 25h + 2h2 = 0 Solving -30 + 25h + 2h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + 12.5h + h2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 12.5h + 15 + h2 = 0 + 15 Reorder the terms: -15 + 15 + 12.5h + h2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 12.5h + h2 = 0 + 15 12.5h + h2 = 0 + 15 Combine like terms: 0 + 15 = 15 12.5h + h2 = 15 The h term is 12.5h. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5h + 39.0625 + h2 = 15 + 39.0625 Reorder the terms: 39.0625 + 12.5h + h2 = 15 + 39.0625 Combine like terms: 15 + 39.0625 = 54.0625 39.0625 + 12.5h + h2 = 54.0625 Factor a perfect square on the left side: (h + 6.25)(h + 6.25) = 54.0625 Calculate the square root of the right side: 7.352720585 Break this problem into two subproblems by setting (h + 6.25) equal to 7.352720585 and -7.352720585.Subproblem 1
h + 6.25 = 7.352720585 Simplifying h + 6.25 = 7.352720585 Reorder the terms: 6.25 + h = 7.352720585 Solving 6.25 + h = 7.352720585 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + h = 7.352720585 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + h = 7.352720585 + -6.25 h = 7.352720585 + -6.25 Combine like terms: 7.352720585 + -6.25 = 1.102720585 h = 1.102720585 Simplifying h = 1.102720585Subproblem 2
h + 6.25 = -7.352720585 Simplifying h + 6.25 = -7.352720585 Reorder the terms: 6.25 + h = -7.352720585 Solving 6.25 + h = -7.352720585 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + h = -7.352720585 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + h = -7.352720585 + -6.25 h = -7.352720585 + -6.25 Combine like terms: -7.352720585 + -6.25 = -13.602720585 h = -13.602720585 Simplifying h = -13.602720585Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.102720585, -13.602720585}
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