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Simplifying h(2h + -4) + (h + 5h + -9) + -1(3h + 7h + -6) = 0 Reorder the terms: h(-4 + 2h) + (h + 5h + -9) + -1(3h + 7h + -6) = 0 (-4 * h + 2h * h) + (h + 5h + -9) + -1(3h + 7h + -6) = 0 (-4h + 2h2) + (h + 5h + -9) + -1(3h + 7h + -6) = 0 Reorder the terms: -4h + 2h2 + (-9 + h + 5h) + -1(3h + 7h + -6) = 0 Combine like terms: h + 5h = 6h -4h + 2h2 + (-9 + 6h) + -1(3h + 7h + -6) = 0 Remove parenthesis around (-9 + 6h) -4h + 2h2 + -9 + 6h + -1(3h + 7h + -6) = 0 Reorder the terms: -4h + 2h2 + -9 + 6h + -1(-6 + 3h + 7h) = 0 Combine like terms: 3h + 7h = 10h -4h + 2h2 + -9 + 6h + -1(-6 + 10h) = 0 -4h + 2h2 + -9 + 6h + (-6 * -1 + 10h * -1) = 0 -4h + 2h2 + -9 + 6h + (6 + -10h) = 0 Reorder the terms: -9 + 6 + -4h + 6h + -10h + 2h2 = 0 Combine like terms: -9 + 6 = -3 -3 + -4h + 6h + -10h + 2h2 = 0 Combine like terms: -4h + 6h = 2h -3 + 2h + -10h + 2h2 = 0 Combine like terms: 2h + -10h = -8h -3 + -8h + 2h2 = 0 Solving -3 + -8h + 2h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -4h + h2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -4h + 1.5 + h2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -4h + h2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -4h + h2 = 0 + 1.5 -4h + h2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -4h + h2 = 1.5 The h term is -4h. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4h + 4 + h2 = 1.5 + 4 Reorder the terms: 4 + -4h + h2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + -4h + h2 = 5.5 Factor a perfect square on the left side: (h + -2)(h + -2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (h + -2) equal to 2.34520788 and -2.34520788.Subproblem 1
h + -2 = 2.34520788 Simplifying h + -2 = 2.34520788 Reorder the terms: -2 + h = 2.34520788 Solving -2 + h = 2.34520788 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + h = 2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + h = 2.34520788 + 2 h = 2.34520788 + 2 Combine like terms: 2.34520788 + 2 = 4.34520788 h = 4.34520788 Simplifying h = 4.34520788Subproblem 2
h + -2 = -2.34520788 Simplifying h + -2 = -2.34520788 Reorder the terms: -2 + h = -2.34520788 Solving -2 + h = -2.34520788 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + h = -2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + h = -2.34520788 + 2 h = -2.34520788 + 2 Combine like terms: -2.34520788 + 2 = -0.34520788 h = -0.34520788 Simplifying h = -0.34520788Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.34520788, -0.34520788}
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