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Simplifying 0.95h2 + 9.5h + -150 = 0 Reorder the terms: -150 + 9.5h + 0.95h2 = 0 Solving -150 + 9.5h + 0.95h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 0.95 the coefficient of the squared term: Divide each side by '0.95'. -157.8947368 + 10h + h2 = 0 Move the constant term to the right: Add '157.8947368' to each side of the equation. -157.8947368 + 10h + 157.8947368 + h2 = 0 + 157.8947368 Reorder the terms: -157.8947368 + 157.8947368 + 10h + h2 = 0 + 157.8947368 Combine like terms: -157.8947368 + 157.8947368 = 0.0000000 0.0000000 + 10h + h2 = 0 + 157.8947368 10h + h2 = 0 + 157.8947368 Combine like terms: 0 + 157.8947368 = 157.8947368 10h + h2 = 157.8947368 The h term is 10h. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10h + 25 + h2 = 157.8947368 + 25 Reorder the terms: 25 + 10h + h2 = 157.8947368 + 25 Combine like terms: 157.8947368 + 25 = 182.8947368 25 + 10h + h2 = 182.8947368 Factor a perfect square on the left side: (h + 5)(h + 5) = 182.8947368 Calculate the square root of the right side: 13.523858059 Break this problem into two subproblems by setting (h + 5) equal to 13.523858059 and -13.523858059.Subproblem 1
h + 5 = 13.523858059 Simplifying h + 5 = 13.523858059 Reorder the terms: 5 + h = 13.523858059 Solving 5 + h = 13.523858059 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = 13.523858059 + -5 Combine like terms: 5 + -5 = 0 0 + h = 13.523858059 + -5 h = 13.523858059 + -5 Combine like terms: 13.523858059 + -5 = 8.523858059 h = 8.523858059 Simplifying h = 8.523858059Subproblem 2
h + 5 = -13.523858059 Simplifying h + 5 = -13.523858059 Reorder the terms: 5 + h = -13.523858059 Solving 5 + h = -13.523858059 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = -13.523858059 + -5 Combine like terms: 5 + -5 = 0 0 + h = -13.523858059 + -5 h = -13.523858059 + -5 Combine like terms: -13.523858059 + -5 = -18.523858059 h = -18.523858059 Simplifying h = -18.523858059Solution
The solution to the problem is based on the solutions from the subproblems. h = {8.523858059, -18.523858059}
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