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Simplifying 4h2 + 2h = 35 Reorder the terms: 2h + 4h2 = 35 Solving 2h + 4h2 = 35 Solving for variable 'h'. Reorder the terms: -35 + 2h + 4h2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 2h + 4h2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 0.5h + h2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 0.5h + 8.75 + h2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 0.5h + h2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 0.5h + h2 = 0 + 8.75 0.5h + h2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 0.5h + h2 = 8.75 The h term is 0.5h. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5h + 0.0625 + h2 = 8.75 + 0.0625 Reorder the terms: 0.0625 + 0.5h + h2 = 8.75 + 0.0625 Combine like terms: 8.75 + 0.0625 = 8.8125 0.0625 + 0.5h + h2 = 8.8125 Factor a perfect square on the left side: (h + 0.25)(h + 0.25) = 8.8125 Calculate the square root of the right side: 2.968585522 Break this problem into two subproblems by setting (h + 0.25) equal to 2.968585522 and -2.968585522.Subproblem 1
h + 0.25 = 2.968585522 Simplifying h + 0.25 = 2.968585522 Reorder the terms: 0.25 + h = 2.968585522 Solving 0.25 + h = 2.968585522 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + h = 2.968585522 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + h = 2.968585522 + -0.25 h = 2.968585522 + -0.25 Combine like terms: 2.968585522 + -0.25 = 2.718585522 h = 2.718585522 Simplifying h = 2.718585522Subproblem 2
h + 0.25 = -2.968585522 Simplifying h + 0.25 = -2.968585522 Reorder the terms: 0.25 + h = -2.968585522 Solving 0.25 + h = -2.968585522 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + h = -2.968585522 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + h = -2.968585522 + -0.25 h = -2.968585522 + -0.25 Combine like terms: -2.968585522 + -0.25 = -3.218585522 h = -3.218585522 Simplifying h = -3.218585522Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.718585522, -3.218585522}
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