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Simplifying -3h2 + 66h = 111 Reorder the terms: 66h + -3h2 = 111 Solving 66h + -3h2 = 111 Solving for variable 'h'. Reorder the terms: -111 + 66h + -3h2 = 111 + -111 Combine like terms: 111 + -111 = 0 -111 + 66h + -3h2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-37 + 22h + -1h2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-37 + 22h + -1h2)' equal to zero and attempt to solve: Simplifying -37 + 22h + -1h2 = 0 Solving -37 + 22h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 37 + -22h + h2 = 0 Move the constant term to the right: Add '-37' to each side of the equation. 37 + -22h + -37 + h2 = 0 + -37 Reorder the terms: 37 + -37 + -22h + h2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -22h + h2 = 0 + -37 -22h + h2 = 0 + -37 Combine like terms: 0 + -37 = -37 -22h + h2 = -37 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 = -37 + 121 Reorder the terms: 121 + -22h + h2 = -37 + 121 Combine like terms: -37 + 121 = 84 121 + -22h + h2 = 84 Factor a perfect square on the left side: (h + -11)(h + -11) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (h + -11) equal to 9.16515139 and -9.16515139.Subproblem 1
h + -11 = 9.16515139 Simplifying h + -11 = 9.16515139 Reorder the terms: -11 + h = 9.16515139 Solving -11 + h = 9.16515139 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 = 9.16515139 + 11 Combine like terms: -11 + 11 = 0 0 + h = 9.16515139 + 11 h = 9.16515139 + 11 Combine like terms: 9.16515139 + 11 = 20.16515139 h = 20.16515139 Simplifying h = 20.16515139Subproblem 2
h + -11 = -9.16515139 Simplifying h + -11 = -9.16515139 Reorder the terms: -11 + h = -9.16515139 Solving -11 + h = -9.16515139 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 = -9.16515139 + 11 Combine like terms: -11 + 11 = 0 0 + h = -9.16515139 + 11 h = -9.16515139 + 11 Combine like terms: -9.16515139 + 11 = 1.83484861 h = 1.83484861 Simplifying h = 1.83484861Solution
The solution to the problem is based on the solutions from the subproblems. h = {20.16515139, 1.83484861}Solution
h = {20.16515139, 1.83484861}
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