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Simplifying h2 + 81h + 18 = 3 Reorder the terms: 18 + 81h + h2 = 3 Solving 18 + 81h + h2 = 3 Solving for variable 'h'. Reorder the terms: 18 + -3 + 81h + h2 = 3 + -3 Combine like terms: 18 + -3 = 15 15 + 81h + h2 = 3 + -3 Combine like terms: 3 + -3 = 0 15 + 81h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 81h + -15 + h2 = 0 + -15 Reorder the terms: 15 + -15 + 81h + h2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 81h + h2 = 0 + -15 81h + h2 = 0 + -15 Combine like terms: 0 + -15 = -15 81h + h2 = -15 The h term is 81h. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81h + 1640.25 + h2 = -15 + 1640.25 Reorder the terms: 1640.25 + 81h + h2 = -15 + 1640.25 Combine like terms: -15 + 1640.25 = 1625.25 1640.25 + 81h + h2 = 1625.25 Factor a perfect square on the left side: (h + 40.5)(h + 40.5) = 1625.25 Calculate the square root of the right side: 40.314389491 Break this problem into two subproblems by setting (h + 40.5) equal to 40.314389491 and -40.314389491.Subproblem 1
h + 40.5 = 40.314389491 Simplifying h + 40.5 = 40.314389491 Reorder the terms: 40.5 + h = 40.314389491 Solving 40.5 + h = 40.314389491 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + h = 40.314389491 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + h = 40.314389491 + -40.5 h = 40.314389491 + -40.5 Combine like terms: 40.314389491 + -40.5 = -0.185610509 h = -0.185610509 Simplifying h = -0.185610509Subproblem 2
h + 40.5 = -40.314389491 Simplifying h + 40.5 = -40.314389491 Reorder the terms: 40.5 + h = -40.314389491 Solving 40.5 + h = -40.314389491 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + h = -40.314389491 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + h = -40.314389491 + -40.5 h = -40.314389491 + -40.5 Combine like terms: -40.314389491 + -40.5 = -80.814389491 h = -80.814389491 Simplifying h = -80.814389491Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.185610509, -80.814389491}
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