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Simplifying 5h + 2h2 = 27 Solving 5h + 2h2 = 27 Solving for variable 'h'. Reorder the terms: -27 + 5h + 2h2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 5h + 2h2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 2.5h + h2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 2.5h + 13.5 + h2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 2.5h + h2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 2.5h + h2 = 0 + 13.5 2.5h + h2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 2.5h + h2 = 13.5 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 = 13.5 + 1.5625 Reorder the terms: 1.5625 + 2.5h + h2 = 13.5 + 1.5625 Combine like terms: 13.5 + 1.5625 = 15.0625 1.5625 + 2.5h + h2 = 15.0625 Factor a perfect square on the left side: (h + 1.25)(h + 1.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (h + 1.25) equal to 3.881043674 and -3.881043674.Subproblem 1
h + 1.25 = 3.881043674 Simplifying h + 1.25 = 3.881043674 Reorder the terms: 1.25 + h = 3.881043674 Solving 1.25 + h = 3.881043674 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 = 3.881043674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + h = 3.881043674 + -1.25 h = 3.881043674 + -1.25 Combine like terms: 3.881043674 + -1.25 = 2.631043674 h = 2.631043674 Simplifying h = 2.631043674Subproblem 2
h + 1.25 = -3.881043674 Simplifying h + 1.25 = -3.881043674 Reorder the terms: 1.25 + h = -3.881043674 Solving 1.25 + h = -3.881043674 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 = -3.881043674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + h = -3.881043674 + -1.25 h = -3.881043674 + -1.25 Combine like terms: -3.881043674 + -1.25 = -5.131043674 h = -5.131043674 Simplifying h = -5.131043674Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.631043674, -5.131043674}
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