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Simplifying h2 + 18h + -72 = 0 Reorder the terms: -72 + 18h + h2 = 0 Solving -72 + 18h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 18h + 72 + h2 = 0 + 72 Reorder the terms: -72 + 72 + 18h + h2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 18h + h2 = 0 + 72 18h + h2 = 0 + 72 Combine like terms: 0 + 72 = 72 18h + h2 = 72 The h term is 18h. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18h + 81 + h2 = 72 + 81 Reorder the terms: 81 + 18h + h2 = 72 + 81 Combine like terms: 72 + 81 = 153 81 + 18h + h2 = 153 Factor a perfect square on the left side: (h + 9)(h + 9) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (h + 9) equal to 12.369316877 and -12.369316877.Subproblem 1
h + 9 = 12.369316877 Simplifying h + 9 = 12.369316877 Reorder the terms: 9 + h = 12.369316877 Solving 9 + h = 12.369316877 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + h = 12.369316877 + -9 Combine like terms: 9 + -9 = 0 0 + h = 12.369316877 + -9 h = 12.369316877 + -9 Combine like terms: 12.369316877 + -9 = 3.369316877 h = 3.369316877 Simplifying h = 3.369316877Subproblem 2
h + 9 = -12.369316877 Simplifying h + 9 = -12.369316877 Reorder the terms: 9 + h = -12.369316877 Solving 9 + h = -12.369316877 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + h = -12.369316877 + -9 Combine like terms: 9 + -9 = 0 0 + h = -12.369316877 + -9 h = -12.369316877 + -9 Combine like terms: -12.369316877 + -9 = -21.369316877 h = -21.369316877 Simplifying h = -21.369316877Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.369316877, -21.369316877}
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