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Simplifying h2 + -26h = -9 Reorder the terms: -26h + h2 = -9 Solving -26h + h2 = -9 Solving for variable 'h'. Reorder the terms: 9 + -26h + h2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -26h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -26h + -9 + h2 = 0 + -9 Reorder the terms: 9 + -9 + -26h + h2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -26h + h2 = 0 + -9 -26h + h2 = 0 + -9 Combine like terms: 0 + -9 = -9 -26h + h2 = -9 The h term is -26h. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26h + 169 + h2 = -9 + 169 Reorder the terms: 169 + -26h + h2 = -9 + 169 Combine like terms: -9 + 169 = 160 169 + -26h + h2 = 160 Factor a perfect square on the left side: (h + -13)(h + -13) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (h + -13) equal to 12.649110641 and -12.649110641.Subproblem 1
h + -13 = 12.649110641 Simplifying h + -13 = 12.649110641 Reorder the terms: -13 + h = 12.649110641 Solving -13 + h = 12.649110641 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + h = 12.649110641 + 13 Combine like terms: -13 + 13 = 0 0 + h = 12.649110641 + 13 h = 12.649110641 + 13 Combine like terms: 12.649110641 + 13 = 25.649110641 h = 25.649110641 Simplifying h = 25.649110641Subproblem 2
h + -13 = -12.649110641 Simplifying h + -13 = -12.649110641 Reorder the terms: -13 + h = -12.649110641 Solving -13 + h = -12.649110641 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + h = -12.649110641 + 13 Combine like terms: -13 + 13 = 0 0 + h = -12.649110641 + 13 h = -12.649110641 + 13 Combine like terms: -12.649110641 + 13 = 0.350889359 h = 0.350889359 Simplifying h = 0.350889359Solution
The solution to the problem is based on the solutions from the subproblems. h = {25.649110641, 0.350889359}
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