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Simplifying -3h2 + -66h = 147 Reorder the terms: -66h + -3h2 = 147 Solving -66h + -3h2 = 147 Solving for variable 'h'. Reorder the terms: -147 + -66h + -3h2 = 147 + -147 Combine like terms: 147 + -147 = 0 -147 + -66h + -3h2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(49 + 22h + h2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(49 + 22h + h2)' equal to zero and attempt to solve: Simplifying 49 + 22h + h2 = 0 Solving 49 + 22h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + 22h + -49 + h2 = 0 + -49 Reorder the terms: 49 + -49 + 22h + h2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 22h + h2 = 0 + -49 22h + h2 = 0 + -49 Combine like terms: 0 + -49 = -49 22h + h2 = -49 The h term is 22h. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22h + 121 + h2 = -49 + 121 Reorder the terms: 121 + 22h + h2 = -49 + 121 Combine like terms: -49 + 121 = 72 121 + 22h + h2 = 72 Factor a perfect square on the left side: (h + 11)(h + 11) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (h + 11) equal to 8.485281374 and -8.485281374.Subproblem 1
h + 11 = 8.485281374 Simplifying h + 11 = 8.485281374 Reorder the terms: 11 + h = 8.485281374 Solving 11 + h = 8.485281374 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + h = 8.485281374 + -11 Combine like terms: 11 + -11 = 0 0 + h = 8.485281374 + -11 h = 8.485281374 + -11 Combine like terms: 8.485281374 + -11 = -2.514718626 h = -2.514718626 Simplifying h = -2.514718626Subproblem 2
h + 11 = -8.485281374 Simplifying h + 11 = -8.485281374 Reorder the terms: 11 + h = -8.485281374 Solving 11 + h = -8.485281374 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + h = -8.485281374 + -11 Combine like terms: 11 + -11 = 0 0 + h = -8.485281374 + -11 h = -8.485281374 + -11 Combine like terms: -8.485281374 + -11 = -19.485281374 h = -19.485281374 Simplifying h = -19.485281374Solution
The solution to the problem is based on the solutions from the subproblems. h = {-2.514718626, -19.485281374}Solution
h = {-2.514718626, -19.485281374}
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