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Simplifying -4.9h2 + 29h + 19 = 0 Reorder the terms: 19 + 29h + -4.9h2 = 0 Solving 19 + 29h + -4.9h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -3.87755102 + -5.918367347h + h2 = 0 Move the constant term to the right: Add '3.87755102' to each side of the equation. -3.87755102 + -5.918367347h + 3.87755102 + h2 = 0 + 3.87755102 Reorder the terms: -3.87755102 + 3.87755102 + -5.918367347h + h2 = 0 + 3.87755102 Combine like terms: -3.87755102 + 3.87755102 = 0.00000000 0.00000000 + -5.918367347h + h2 = 0 + 3.87755102 -5.918367347h + h2 = 0 + 3.87755102 Combine like terms: 0 + 3.87755102 = 3.87755102 -5.918367347h + h2 = 3.87755102 The h term is -5.918367347h. Take half its coefficient (-2.959183674). Square it (8.756768016) and add it to both sides. Add '8.756768016' to each side of the equation. -5.918367347h + 8.756768016 + h2 = 3.87755102 + 8.756768016 Reorder the terms: 8.756768016 + -5.918367347h + h2 = 3.87755102 + 8.756768016 Combine like terms: 3.87755102 + 8.756768016 = 12.634319036 8.756768016 + -5.918367347h + h2 = 12.634319036 Factor a perfect square on the left side: (h + -2.959183674)(h + -2.959183674) = 12.634319036 Calculate the square root of the right side: 3.554478729 Break this problem into two subproblems by setting (h + -2.959183674) equal to 3.554478729 and -3.554478729.Subproblem 1
h + -2.959183674 = 3.554478729 Simplifying h + -2.959183674 = 3.554478729 Reorder the terms: -2.959183674 + h = 3.554478729 Solving -2.959183674 + h = 3.554478729 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.959183674' to each side of the equation. -2.959183674 + 2.959183674 + h = 3.554478729 + 2.959183674 Combine like terms: -2.959183674 + 2.959183674 = 0.000000000 0.000000000 + h = 3.554478729 + 2.959183674 h = 3.554478729 + 2.959183674 Combine like terms: 3.554478729 + 2.959183674 = 6.513662403 h = 6.513662403 Simplifying h = 6.513662403Subproblem 2
h + -2.959183674 = -3.554478729 Simplifying h + -2.959183674 = -3.554478729 Reorder the terms: -2.959183674 + h = -3.554478729 Solving -2.959183674 + h = -3.554478729 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.959183674' to each side of the equation. -2.959183674 + 2.959183674 + h = -3.554478729 + 2.959183674 Combine like terms: -2.959183674 + 2.959183674 = 0.000000000 0.000000000 + h = -3.554478729 + 2.959183674 h = -3.554478729 + 2.959183674 Combine like terms: -3.554478729 + 2.959183674 = -0.595295055 h = -0.595295055 Simplifying h = -0.595295055Solution
The solution to the problem is based on the solutions from the subproblems. h = {6.513662403, -0.595295055}
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