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Simplifying h2 + -27h + 108 = 0 Reorder the terms: 108 + -27h + h2 = 0 Solving 108 + -27h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + -27h + -108 + h2 = 0 + -108 Reorder the terms: 108 + -108 + -27h + h2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + -27h + h2 = 0 + -108 -27h + h2 = 0 + -108 Combine like terms: 0 + -108 = -108 -27h + h2 = -108 The h term is -27h. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27h + 182.25 + h2 = -108 + 182.25 Reorder the terms: 182.25 + -27h + h2 = -108 + 182.25 Combine like terms: -108 + 182.25 = 74.25 182.25 + -27h + h2 = 74.25 Factor a perfect square on the left side: (h + -13.5)(h + -13.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (h + -13.5) equal to 8.61684397 and -8.61684397.Subproblem 1
h + -13.5 = 8.61684397 Simplifying h + -13.5 = 8.61684397 Reorder the terms: -13.5 + h = 8.61684397 Solving -13.5 + h = 8.61684397 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + h = 8.61684397 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + h = 8.61684397 + 13.5 h = 8.61684397 + 13.5 Combine like terms: 8.61684397 + 13.5 = 22.11684397 h = 22.11684397 Simplifying h = 22.11684397Subproblem 2
h + -13.5 = -8.61684397 Simplifying h + -13.5 = -8.61684397 Reorder the terms: -13.5 + h = -8.61684397 Solving -13.5 + h = -8.61684397 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + h = -8.61684397 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + h = -8.61684397 + 13.5 h = -8.61684397 + 13.5 Combine like terms: -8.61684397 + 13.5 = 4.88315603 h = 4.88315603 Simplifying h = 4.88315603Solution
The solution to the problem is based on the solutions from the subproblems. h = {22.11684397, 4.88315603}
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