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Simplifying h2 + -18h + 13 = 0 Reorder the terms: 13 + -18h + h2 = 0 Solving 13 + -18h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -18h + -13 + h2 = 0 + -13 Reorder the terms: 13 + -13 + -18h + h2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -18h + h2 = 0 + -13 -18h + h2 = 0 + -13 Combine like terms: 0 + -13 = -13 -18h + h2 = -13 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 = -13 + 81 Reorder the terms: 81 + -18h + h2 = -13 + 81 Combine like terms: -13 + 81 = 68 81 + -18h + h2 = 68 Factor a perfect square on the left side: (h + -9)(h + -9) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (h + -9) equal to 8.246211251 and -8.246211251.Subproblem 1
h + -9 = 8.246211251 Simplifying h + -9 = 8.246211251 Reorder the terms: -9 + h = 8.246211251 Solving -9 + h = 8.246211251 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 = 8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + h = 8.246211251 + 9 h = 8.246211251 + 9 Combine like terms: 8.246211251 + 9 = 17.246211251 h = 17.246211251 Simplifying h = 17.246211251Subproblem 2
h + -9 = -8.246211251 Simplifying h + -9 = -8.246211251 Reorder the terms: -9 + h = -8.246211251 Solving -9 + h = -8.246211251 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 = -8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + h = -8.246211251 + 9 h = -8.246211251 + 9 Combine like terms: -8.246211251 + 9 = 0.753788749 h = 0.753788749 Simplifying h = 0.753788749Solution
The solution to the problem is based on the solutions from the subproblems. h = {17.246211251, 0.753788749}
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