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Simplifying 5h(h + -2) = 3h + 2 Reorder the terms: 5h(-2 + h) = 3h + 2 (-2 * 5h + h * 5h) = 3h + 2 (-10h + 5h2) = 3h + 2 Reorder the terms: -10h + 5h2 = 2 + 3h Solving -10h + 5h2 = 2 + 3h Solving for variable 'h'. Reorder the terms: -2 + -10h + -3h + 5h2 = 2 + 3h + -2 + -3h Combine like terms: -10h + -3h = -13h -2 + -13h + 5h2 = 2 + 3h + -2 + -3h Reorder the terms: -2 + -13h + 5h2 = 2 + -2 + 3h + -3h Combine like terms: 2 + -2 = 0 -2 + -13h + 5h2 = 0 + 3h + -3h -2 + -13h + 5h2 = 3h + -3h Combine like terms: 3h + -3h = 0 -2 + -13h + 5h2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -2.6h + h2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.6h + 0.4 + h2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.6h + h2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.6h + h2 = 0 + 0.4 -2.6h + h2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.6h + h2 = 0.4 The h term is -2.6h. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6h + 1.69 + h2 = 0.4 + 1.69 Reorder the terms: 1.69 + -2.6h + h2 = 0.4 + 1.69 Combine like terms: 0.4 + 1.69 = 2.09 1.69 + -2.6h + h2 = 2.09 Factor a perfect square on the left side: (h + -1.3)(h + -1.3) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (h + -1.3) equal to 1.445683229 and -1.445683229.Subproblem 1
h + -1.3 = 1.445683229 Simplifying h + -1.3 = 1.445683229 Reorder the terms: -1.3 + h = 1.445683229 Solving -1.3 + h = 1.445683229 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + h = 1.445683229 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + h = 1.445683229 + 1.3 h = 1.445683229 + 1.3 Combine like terms: 1.445683229 + 1.3 = 2.745683229 h = 2.745683229 Simplifying h = 2.745683229Subproblem 2
h + -1.3 = -1.445683229 Simplifying h + -1.3 = -1.445683229 Reorder the terms: -1.3 + h = -1.445683229 Solving -1.3 + h = -1.445683229 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + h = -1.445683229 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + h = -1.445683229 + 1.3 h = -1.445683229 + 1.3 Combine like terms: -1.445683229 + 1.3 = -0.145683229 h = -0.145683229 Simplifying h = -0.145683229Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.745683229, -0.145683229}
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