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Simplifying 0 = 3h2 + 44h + -6256 Reorder the terms: 0 = -6256 + 44h + 3h2 Solving 0 = -6256 + 44h + 3h2 Solving for variable 'h'. Combine like terms: 0 + 6256 = 6256 6256 + -44h + -3h2 = -6256 + 44h + 3h2 + 6256 + -44h + -3h2 Reorder the terms: 6256 + -44h + -3h2 = -6256 + 6256 + 44h + -44h + 3h2 + -3h2 Combine like terms: -6256 + 6256 = 0 6256 + -44h + -3h2 = 0 + 44h + -44h + 3h2 + -3h2 6256 + -44h + -3h2 = 44h + -44h + 3h2 + -3h2 Combine like terms: 44h + -44h = 0 6256 + -44h + -3h2 = 0 + 3h2 + -3h2 6256 + -44h + -3h2 = 3h2 + -3h2 Combine like terms: 3h2 + -3h2 = 0 6256 + -44h + -3h2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2085.333333 + 14.66666667h + h2 = 0 Move the constant term to the right: Add '2085.333333' to each side of the equation. -2085.333333 + 14.66666667h + 2085.333333 + h2 = 0 + 2085.333333 Reorder the terms: -2085.333333 + 2085.333333 + 14.66666667h + h2 = 0 + 2085.333333 Combine like terms: -2085.333333 + 2085.333333 = 0.000000 0.000000 + 14.66666667h + h2 = 0 + 2085.333333 14.66666667h + h2 = 0 + 2085.333333 Combine like terms: 0 + 2085.333333 = 2085.333333 14.66666667h + h2 = 2085.333333 The h term is 14.66666667h. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667h + 53.77777780 + h2 = 2085.333333 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667h + h2 = 2085.333333 + 53.77777780 Combine like terms: 2085.333333 + 53.77777780 = 2139.1111108 53.77777780 + 14.66666667h + h2 = 2139.1111108 Factor a perfect square on the left side: (h + 7.333333335)(h + 7.333333335) = 2139.1111108 Calculate the square root of the right side: 46.250525519 Break this problem into two subproblems by setting (h + 7.333333335) equal to 46.250525519 and -46.250525519.Subproblem 1
h + 7.333333335 = 46.250525519 Simplifying h + 7.333333335 = 46.250525519 Reorder the terms: 7.333333335 + h = 46.250525519 Solving 7.333333335 + h = 46.250525519 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + h = 46.250525519 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + h = 46.250525519 + -7.333333335 h = 46.250525519 + -7.333333335 Combine like terms: 46.250525519 + -7.333333335 = 38.917192184 h = 38.917192184 Simplifying h = 38.917192184Subproblem 2
h + 7.333333335 = -46.250525519 Simplifying h + 7.333333335 = -46.250525519 Reorder the terms: 7.333333335 + h = -46.250525519 Solving 7.333333335 + h = -46.250525519 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + h = -46.250525519 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + h = -46.250525519 + -7.333333335 h = -46.250525519 + -7.333333335 Combine like terms: -46.250525519 + -7.333333335 = -53.583858854 h = -53.583858854 Simplifying h = -53.583858854Solution
The solution to the problem is based on the solutions from the subproblems. h = {38.917192184, -53.583858854}
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