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Simplifying x2 + 36x = 231 Reorder the terms: 36x + x2 = 231 Solving 36x + x2 = 231 Solving for variable 'x'. Reorder the terms: -231 + 36x + x2 = 231 + -231 Combine like terms: 231 + -231 = 0 -231 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '231' to each side of the equation. -231 + 36x + 231 + x2 = 0 + 231 Reorder the terms: -231 + 231 + 36x + x2 = 0 + 231 Combine like terms: -231 + 231 = 0 0 + 36x + x2 = 0 + 231 36x + x2 = 0 + 231 Combine like terms: 0 + 231 = 231 36x + x2 = 231 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 231 + 324 Reorder the terms: 324 + 36x + x2 = 231 + 324 Combine like terms: 231 + 324 = 555 324 + 36x + x2 = 555 Factor a perfect square on the left side: (x + 18)(x + 18) = 555 Calculate the square root of the right side: 23.558437979 Break this problem into two subproblems by setting (x + 18) equal to 23.558437979 and -23.558437979.Subproblem 1
x + 18 = 23.558437979 Simplifying x + 18 = 23.558437979 Reorder the terms: 18 + x = 23.558437979 Solving 18 + x = 23.558437979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 23.558437979 + -18 Combine like terms: 18 + -18 = 0 0 + x = 23.558437979 + -18 x = 23.558437979 + -18 Combine like terms: 23.558437979 + -18 = 5.558437979 x = 5.558437979 Simplifying x = 5.558437979Subproblem 2
x + 18 = -23.558437979 Simplifying x + 18 = -23.558437979 Reorder the terms: 18 + x = -23.558437979 Solving 18 + x = -23.558437979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -23.558437979 + -18 Combine like terms: 18 + -18 = 0 0 + x = -23.558437979 + -18 x = -23.558437979 + -18 Combine like terms: -23.558437979 + -18 = -41.558437979 x = -41.558437979 Simplifying x = -41.558437979Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.558437979, -41.558437979}
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