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Simplifying 2h2 + 5h + 2 = 605.625 Reorder the terms: 2 + 5h + 2h2 = 605.625 Solving 2 + 5h + 2h2 = 605.625 Solving for variable 'h'. Reorder the terms: 2 + -605.625 + 5h + 2h2 = 605.625 + -605.625 Combine like terms: 2 + -605.625 = -603.625 -603.625 + 5h + 2h2 = 605.625 + -605.625 Combine like terms: 605.625 + -605.625 = 0.000 -603.625 + 5h + 2h2 = 0.000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -301.8125 + 2.5h + h2 = 0.000 Move the constant term to the right: Add '301.8125' to each side of the equation. -301.8125 + 2.5h + 301.8125 + h2 = 0.000 + 301.8125 Reorder the terms: -301.8125 + 301.8125 + 2.5h + h2 = 0.000 + 301.8125 Combine like terms: -301.8125 + 301.8125 = 0.0000 0.0000 + 2.5h + h2 = 0.000 + 301.8125 2.5h + h2 = 0.000 + 301.8125 Combine like terms: 0.000 + 301.8125 = 301.8125 2.5h + h2 = 301.8125 The h term is 2.5h. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5h + 1.5625 + h2 = 301.8125 + 1.5625 Reorder the terms: 1.5625 + 2.5h + h2 = 301.8125 + 1.5625 Combine like terms: 301.8125 + 1.5625 = 303.375 1.5625 + 2.5h + h2 = 303.375 Factor a perfect square on the left side: (h + 1.25)(h + 1.25) = 303.375 Calculate the square root of the right side: 17.417663448 Break this problem into two subproblems by setting (h + 1.25) equal to 17.417663448 and -17.417663448.Subproblem 1
h + 1.25 = 17.417663448 Simplifying h + 1.25 = 17.417663448 Reorder the terms: 1.25 + h = 17.417663448 Solving 1.25 + h = 17.417663448 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + h = 17.417663448 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + h = 17.417663448 + -1.25 h = 17.417663448 + -1.25 Combine like terms: 17.417663448 + -1.25 = 16.167663448 h = 16.167663448 Simplifying h = 16.167663448Subproblem 2
h + 1.25 = -17.417663448 Simplifying h + 1.25 = -17.417663448 Reorder the terms: 1.25 + h = -17.417663448 Solving 1.25 + h = -17.417663448 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + h = -17.417663448 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + h = -17.417663448 + -1.25 h = -17.417663448 + -1.25 Combine like terms: -17.417663448 + -1.25 = -18.667663448 h = -18.667663448 Simplifying h = -18.667663448Solution
The solution to the problem is based on the solutions from the subproblems. h = {16.167663448, -18.667663448}
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