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Simplifying 3h2 + 8h + -4896 = 0 Reorder the terms: -4896 + 8h + 3h2 = 0 Solving -4896 + 8h + 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'. -1632 + 2.666666667h + h2 = 0 Move the constant term to the right: Add '1632' to each side of the equation. -1632 + 2.666666667h + 1632 + h2 = 0 + 1632 Reorder the terms: -1632 + 1632 + 2.666666667h + h2 = 0 + 1632 Combine like terms: -1632 + 1632 = 0 0 + 2.666666667h + h2 = 0 + 1632 2.666666667h + h2 = 0 + 1632 Combine like terms: 0 + 1632 = 1632 2.666666667h + h2 = 1632 The h term is 2.666666667h. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667h + 1.777777780 + h2 = 1632 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667h + h2 = 1632 + 1.777777780 Combine like terms: 1632 + 1.777777780 = 1633.77777778 1.777777780 + 2.666666667h + h2 = 1633.77777778 Factor a perfect square on the left side: (h + 1.333333334)(h + 1.333333334) = 1633.77777778 Calculate the square root of the right side: 40.420017043 Break this problem into two subproblems by setting (h + 1.333333334) equal to 40.420017043 and -40.420017043.Subproblem 1
h + 1.333333334 = 40.420017043 Simplifying h + 1.333333334 = 40.420017043 Reorder the terms: 1.333333334 + h = 40.420017043 Solving 1.333333334 + h = 40.420017043 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + h = 40.420017043 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + h = 40.420017043 + -1.333333334 h = 40.420017043 + -1.333333334 Combine like terms: 40.420017043 + -1.333333334 = 39.086683709 h = 39.086683709 Simplifying h = 39.086683709Subproblem 2
h + 1.333333334 = -40.420017043 Simplifying h + 1.333333334 = -40.420017043 Reorder the terms: 1.333333334 + h = -40.420017043 Solving 1.333333334 + h = -40.420017043 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + h = -40.420017043 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + h = -40.420017043 + -1.333333334 h = -40.420017043 + -1.333333334 Combine like terms: -40.420017043 + -1.333333334 = -41.753350377 h = -41.753350377 Simplifying h = -41.753350377Solution
The solution to the problem is based on the solutions from the subproblems. h = {39.086683709, -41.753350377}
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