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Simplifying h2 + 18h + -8 = 0 Reorder the terms: -8 + 18h + h2 = 0 Solving -8 + 18h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 18h + 8 + h2 = 0 + 8 Reorder the terms: -8 + 8 + 18h + h2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 18h + h2 = 0 + 8 18h + h2 = 0 + 8 Combine like terms: 0 + 8 = 8 18h + h2 = 8 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 = 8 + 81 Reorder the terms: 81 + 18h + h2 = 8 + 81 Combine like terms: 8 + 81 = 89 81 + 18h + h2 = 89 Factor a perfect square on the left side: (h + 9)(h + 9) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (h + 9) equal to 9.433981132 and -9.433981132.Subproblem 1
h + 9 = 9.433981132 Simplifying h + 9 = 9.433981132 Reorder the terms: 9 + h = 9.433981132 Solving 9 + h = 9.433981132 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 = 9.433981132 + -9 Combine like terms: 9 + -9 = 0 0 + h = 9.433981132 + -9 h = 9.433981132 + -9 Combine like terms: 9.433981132 + -9 = 0.433981132 h = 0.433981132 Simplifying h = 0.433981132Subproblem 2
h + 9 = -9.433981132 Simplifying h + 9 = -9.433981132 Reorder the terms: 9 + h = -9.433981132 Solving 9 + h = -9.433981132 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 = -9.433981132 + -9 Combine like terms: 9 + -9 = 0 0 + h = -9.433981132 + -9 h = -9.433981132 + -9 Combine like terms: -9.433981132 + -9 = -18.433981132 h = -18.433981132 Simplifying h = -18.433981132Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.433981132, -18.433981132}
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