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Simplifying 0 = (1.39h2) + -1(1141.6h) + -1222849 Remove parenthesis around (1141.6h) 0 = (1.39h2) + -1 * 1141.6h + -1222849 Multiply -1 * 1141.6 0 = (1.39h2) + -1141.6h + -1222849 Reorder the terms: 0 = -1222849 + -1141.6h + (1.39h2) Solving 0 = -1222849 + -1141.6h + (1.39h2) Solving for variable 'h'. Combine like terms: 0 + 1222849 = 1222849 1222849 + 1141.6h + (-1.39h2) = -1222849 + -1141.6h + (1.39h2) + 1222849 + 1141.6h + (-1.39h2) Reorder the terms: 1222849 + 1141.6h + (-1.39h2) = -1222849 + 1222849 + -1141.6h + 1141.6h + (1.39h2) + (-1.39h2) Combine like terms: -1222849 + 1222849 = 0 1222849 + 1141.6h + (-1.39h2) = 0 + -1141.6h + 1141.6h + (1.39h2) + (-1.39h2) 1222849 + 1141.6h + (-1.39h2) = -1141.6h + 1141.6h + (1.39h2) + (-1.39h2) Combine like terms: -1141.6h + 1141.6h = 0.0 1222849 + 1141.6h + (-1.39h2) = 0.0 + (1.39h2) + (-1.39h2) 1222849 + 1141.6h + (-1.39h2) = (1.39h2) + (-1.39h2) Combine like terms: (1.39h2) + (-1.39h2) = 0.00 1222849 + 1141.6h + (-1.39h2) = 0.00 Begin completing the square. Divide all terms by -1.39 the coefficient of the squared term: Divide each side by '-1.39'. -879747.482 + -821.294964h + h2 = 0 Move the constant term to the right: Add '879747.482' to each side of the equation. -879747.482 + -821.294964h + 879747.482 + h2 = 0 + 879747.482 Reorder the terms: -879747.482 + 879747.482 + -821.294964h + h2 = 0 + 879747.482 Combine like terms: -879747.482 + 879747.482 = 0.000 0.000 + -821.294964h + h2 = 0 + 879747.482 -821.294964h + h2 = 0 + 879747.482 Combine like terms: 0 + 879747.482 = 879747.482 -821.294964h + h2 = 879747.482 The h term is -821.294964h. Take half its coefficient (-410.647482). Square it (168631.3545) and add it to both sides. Add '168631.3545' to each side of the equation. -821.294964h + 168631.3545 + h2 = 879747.482 + 168631.3545 Reorder the terms: 168631.3545 + -821.294964h + h2 = 879747.482 + 168631.3545 Combine like terms: 879747.482 + 168631.3545 = 1048378.8365 168631.3545 + -821.294964h + h2 = 1048378.8365 Factor a perfect square on the left side: ((h) + -410.647482)((h) + -410.647482) = 1048378.8365 Calculate the square root of the right side: 1023.903724234 Break this problem into two subproblems by setting ((h) + -410.647482) equal to 1023.903724234 and -1023.903724234.Subproblem 1
(h) + -410.647482 = 1023.903724234 Simplifying (h) + -410.647482 = 1023.903724234 h + -410.647482 = 1023.903724234 Reorder the terms: -410.647482 + h = 1023.903724234 Solving -410.647482 + h = 1023.903724234 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '410.647482' to each side of the equation. -410.647482 + 410.647482 + h = 1023.903724234 + 410.647482 Combine like terms: -410.647482 + 410.647482 = 0.000000 0.000000 + h = 1023.903724234 + 410.647482 h = 1023.903724234 + 410.647482 Combine like terms: 1023.903724234 + 410.647482 = 1434.551206234 h = 1434.551206234 Simplifying h = 1434.551206234Subproblem 2
(h) + -410.647482 = -1023.903724234 Simplifying (h) + -410.647482 = -1023.903724234 h + -410.647482 = -1023.903724234 Reorder the terms: -410.647482 + h = -1023.903724234 Solving -410.647482 + h = -1023.903724234 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '410.647482' to each side of the equation. -410.647482 + 410.647482 + h = -1023.903724234 + 410.647482 Combine like terms: -410.647482 + 410.647482 = 0.000000 0.000000 + h = -1023.903724234 + 410.647482 h = -1023.903724234 + 410.647482 Combine like terms: -1023.903724234 + 410.647482 = -613.256242234 h = -613.256242234 Simplifying h = -613.256242234Solution
The solution to the problem is based on the solutions from the subproblems. h = {1434.551206234, -613.256242234}
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