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Simplifying h2 + 99h + 18 = 0 Reorder the terms: 18 + 99h + h2 = 0 Solving 18 + 99h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 99h + -18 + h2 = 0 + -18 Reorder the terms: 18 + -18 + 99h + h2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 99h + h2 = 0 + -18 99h + h2 = 0 + -18 Combine like terms: 0 + -18 = -18 99h + h2 = -18 The h term is 99h. Take half its coefficient (49.5). Square it (2450.25) and add it to both sides. Add '2450.25' to each side of the equation. 99h + 2450.25 + h2 = -18 + 2450.25 Reorder the terms: 2450.25 + 99h + h2 = -18 + 2450.25 Combine like terms: -18 + 2450.25 = 2432.25 2450.25 + 99h + h2 = 2432.25 Factor a perfect square on the left side: (h + 49.5)(h + 49.5) = 2432.25 Calculate the square root of the right side: 49.317846668 Break this problem into two subproblems by setting (h + 49.5) equal to 49.317846668 and -49.317846668.Subproblem 1
h + 49.5 = 49.317846668 Simplifying h + 49.5 = 49.317846668 Reorder the terms: 49.5 + h = 49.317846668 Solving 49.5 + h = 49.317846668 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-49.5' to each side of the equation. 49.5 + -49.5 + h = 49.317846668 + -49.5 Combine like terms: 49.5 + -49.5 = 0.0 0.0 + h = 49.317846668 + -49.5 h = 49.317846668 + -49.5 Combine like terms: 49.317846668 + -49.5 = -0.182153332 h = -0.182153332 Simplifying h = -0.182153332Subproblem 2
h + 49.5 = -49.317846668 Simplifying h + 49.5 = -49.317846668 Reorder the terms: 49.5 + h = -49.317846668 Solving 49.5 + h = -49.317846668 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-49.5' to each side of the equation. 49.5 + -49.5 + h = -49.317846668 + -49.5 Combine like terms: 49.5 + -49.5 = 0.0 0.0 + h = -49.317846668 + -49.5 h = -49.317846668 + -49.5 Combine like terms: -49.317846668 + -49.5 = -98.817846668 h = -98.817846668 Simplifying h = -98.817846668Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.182153332, -98.817846668}
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