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Simplifying h2 + 24h = 17 Reorder the terms: 24h + h2 = 17 Solving 24h + h2 = 17 Solving for variable 'h'. Reorder the terms: -17 + 24h + h2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 24h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 24h + 17 + h2 = 0 + 17 Reorder the terms: -17 + 17 + 24h + h2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 24h + h2 = 0 + 17 24h + h2 = 0 + 17 Combine like terms: 0 + 17 = 17 24h + h2 = 17 The h term is 24h. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24h + 144 + h2 = 17 + 144 Reorder the terms: 144 + 24h + h2 = 17 + 144 Combine like terms: 17 + 144 = 161 144 + 24h + h2 = 161 Factor a perfect square on the left side: (h + 12)(h + 12) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (h + 12) equal to 12.68857754 and -12.68857754.Subproblem 1
h + 12 = 12.68857754 Simplifying h + 12 = 12.68857754 Reorder the terms: 12 + h = 12.68857754 Solving 12 + h = 12.68857754 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + h = 12.68857754 + -12 Combine like terms: 12 + -12 = 0 0 + h = 12.68857754 + -12 h = 12.68857754 + -12 Combine like terms: 12.68857754 + -12 = 0.68857754 h = 0.68857754 Simplifying h = 0.68857754Subproblem 2
h + 12 = -12.68857754 Simplifying h + 12 = -12.68857754 Reorder the terms: 12 + h = -12.68857754 Solving 12 + h = -12.68857754 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + h = -12.68857754 + -12 Combine like terms: 12 + -12 = 0 0 + h = -12.68857754 + -12 h = -12.68857754 + -12 Combine like terms: -12.68857754 + -12 = -24.68857754 h = -24.68857754 Simplifying h = -24.68857754Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.68857754, -24.68857754}
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