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Simplifying -7h + (3h2) + -4h + -3 = 0 Reorder the terms: -3 + -7h + -4h + (3h2) = 0 Combine like terms: -7h + -4h = -11h -3 + -11h + (3h2) = 0 Solving -3 + -11h + (3h2) = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -3.666666667h + h2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.666666667h + 1 + h2 = 0 + 1 Reorder the terms: -1 + 1 + -3.666666667h + h2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.666666667h + h2 = 0 + 1 -3.666666667h + h2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.666666667h + h2 = 1 The h term is -3.666666667h. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667h + 3.361111114 + h2 = 1 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667h + h2 = 1 + 3.361111114 Combine like terms: 1 + 3.361111114 = 4.361111114 3.361111114 + -3.666666667h + h2 = 4.361111114 Factor a perfect square on the left side: ((h) + -1.833333334)((h) + -1.833333334) = 4.361111114 Calculate the square root of the right side: 2.088327348 Break this problem into two subproblems by setting ((h) + -1.833333334) equal to 2.088327348 and -2.088327348.Subproblem 1
(h) + -1.833333334 = 2.088327348 Simplifying (h) + -1.833333334 = 2.088327348 h + -1.833333334 = 2.088327348 Reorder the terms: -1.833333334 + h = 2.088327348 Solving -1.833333334 + h = 2.088327348 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + h = 2.088327348 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + h = 2.088327348 + 1.833333334 h = 2.088327348 + 1.833333334 Combine like terms: 2.088327348 + 1.833333334 = 3.921660682 h = 3.921660682 Simplifying h = 3.921660682Subproblem 2
(h) + -1.833333334 = -2.088327348 Simplifying (h) + -1.833333334 = -2.088327348 h + -1.833333334 = -2.088327348 Reorder the terms: -1.833333334 + h = -2.088327348 Solving -1.833333334 + h = -2.088327348 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + h = -2.088327348 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + h = -2.088327348 + 1.833333334 h = -2.088327348 + 1.833333334 Combine like terms: -2.088327348 + 1.833333334 = -0.254994014 h = -0.254994014 Simplifying h = -0.254994014Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.921660682, -0.254994014}
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