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Simplifying x2 + -36x + 216 = 0 Reorder the terms: 216 + -36x + x2 = 0 Solving 216 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-216' to each side of the equation. 216 + -36x + -216 + x2 = 0 + -216 Reorder the terms: 216 + -216 + -36x + x2 = 0 + -216 Combine like terms: 216 + -216 = 0 0 + -36x + x2 = 0 + -216 -36x + x2 = 0 + -216 Combine like terms: 0 + -216 = -216 -36x + x2 = -216 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 = -216 + 324 Reorder the terms: 324 + -36x + x2 = -216 + 324 Combine like terms: -216 + 324 = 108 324 + -36x + x2 = 108 Factor a perfect square on the left side: (x + -18)(x + -18) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -18) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -18 = 10.392304845 Simplifying x + -18 = 10.392304845 Reorder the terms: -18 + x = 10.392304845 Solving -18 + x = 10.392304845 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 = 10.392304845 + 18 Combine like terms: -18 + 18 = 0 0 + x = 10.392304845 + 18 x = 10.392304845 + 18 Combine like terms: 10.392304845 + 18 = 28.392304845 x = 28.392304845 Simplifying x = 28.392304845Subproblem 2
x + -18 = -10.392304845 Simplifying x + -18 = -10.392304845 Reorder the terms: -18 + x = -10.392304845 Solving -18 + x = -10.392304845 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 = -10.392304845 + 18 Combine like terms: -18 + 18 = 0 0 + x = -10.392304845 + 18 x = -10.392304845 + 18 Combine like terms: -10.392304845 + 18 = 7.607695155 x = 7.607695155 Simplifying x = 7.607695155Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.392304845, 7.607695155}
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