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Simplifying 3h(h + 5) + 4(2h + -3) = 0 Reorder the terms: 3h(5 + h) + 4(2h + -3) = 0 (5 * 3h + h * 3h) + 4(2h + -3) = 0 (15h + 3h2) + 4(2h + -3) = 0 Reorder the terms: 15h + 3h2 + 4(-3 + 2h) = 0 15h + 3h2 + (-3 * 4 + 2h * 4) = 0 15h + 3h2 + (-12 + 8h) = 0 Reorder the terms: -12 + 15h + 8h + 3h2 = 0 Combine like terms: 15h + 8h = 23h -12 + 23h + 3h2 = 0 Solving -12 + 23h + 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'. -4 + 7.666666667h + h2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 7.666666667h + 4 + h2 = 0 + 4 Reorder the terms: -4 + 4 + 7.666666667h + h2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7.666666667h + h2 = 0 + 4 7.666666667h + h2 = 0 + 4 Combine like terms: 0 + 4 = 4 7.666666667h + h2 = 4 The h term is 7.666666667h. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667h + 14.69444445 + h2 = 4 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667h + h2 = 4 + 14.69444445 Combine like terms: 4 + 14.69444445 = 18.69444445 14.69444445 + 7.666666667h + h2 = 18.69444445 Factor a perfect square on the left side: (h + 3.833333334)(h + 3.833333334) = 18.69444445 Calculate the square root of the right side: 4.323707258 Break this problem into two subproblems by setting (h + 3.833333334) equal to 4.323707258 and -4.323707258.Subproblem 1
h + 3.833333334 = 4.323707258 Simplifying h + 3.833333334 = 4.323707258 Reorder the terms: 3.833333334 + h = 4.323707258 Solving 3.833333334 + h = 4.323707258 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + h = 4.323707258 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + h = 4.323707258 + -3.833333334 h = 4.323707258 + -3.833333334 Combine like terms: 4.323707258 + -3.833333334 = 0.490373924 h = 0.490373924 Simplifying h = 0.490373924Subproblem 2
h + 3.833333334 = -4.323707258 Simplifying h + 3.833333334 = -4.323707258 Reorder the terms: 3.833333334 + h = -4.323707258 Solving 3.833333334 + h = -4.323707258 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + h = -4.323707258 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + h = -4.323707258 + -3.833333334 h = -4.323707258 + -3.833333334 Combine like terms: -4.323707258 + -3.833333334 = -8.157040592 h = -8.157040592 Simplifying h = -8.157040592Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.490373924, -8.157040592}
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