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Simplifying 36h + h2 + -1296 = 0 Reorder the terms: -1296 + 36h + h2 = 0 Solving -1296 + 36h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + 36h + 1296 + h2 = 0 + 1296 Reorder the terms: -1296 + 1296 + 36h + h2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + 36h + h2 = 0 + 1296 36h + h2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 36h + h2 = 1296 The h term is 36h. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36h + 324 + h2 = 1296 + 324 Reorder the terms: 324 + 36h + h2 = 1296 + 324 Combine like terms: 1296 + 324 = 1620 324 + 36h + h2 = 1620 Factor a perfect square on the left side: (h + 18)(h + 18) = 1620 Calculate the square root of the right side: 40.249223595 Break this problem into two subproblems by setting (h + 18) equal to 40.249223595 and -40.249223595.Subproblem 1
h + 18 = 40.249223595 Simplifying h + 18 = 40.249223595 Reorder the terms: 18 + h = 40.249223595 Solving 18 + h = 40.249223595 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + h = 40.249223595 + -18 Combine like terms: 18 + -18 = 0 0 + h = 40.249223595 + -18 h = 40.249223595 + -18 Combine like terms: 40.249223595 + -18 = 22.249223595 h = 22.249223595 Simplifying h = 22.249223595Subproblem 2
h + 18 = -40.249223595 Simplifying h + 18 = -40.249223595 Reorder the terms: 18 + h = -40.249223595 Solving 18 + h = -40.249223595 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + h = -40.249223595 + -18 Combine like terms: 18 + -18 = 0 0 + h = -40.249223595 + -18 h = -40.249223595 + -18 Combine like terms: -40.249223595 + -18 = -58.249223595 h = -58.249223595 Simplifying h = -58.249223595Solution
The solution to the problem is based on the solutions from the subproblems. h = {22.249223595, -58.249223595}
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