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Simplifying x2 + -36x + -108 = 0 Reorder the terms: -108 + -36x + x2 = 0 Solving -108 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -36x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -36x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -36x + x2 = 0 + 108 -36x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -36x + x2 = 108 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 = 108 + 324 Reorder the terms: 324 + -36x + x2 = 108 + 324 Combine like terms: 108 + 324 = 432 324 + -36x + x2 = 432 Factor a perfect square on the left side: (x + -18)(x + -18) = 432 Calculate the square root of the right side: 20.784609691 Break this problem into two subproblems by setting (x + -18) equal to 20.784609691 and -20.784609691.Subproblem 1
x + -18 = 20.784609691 Simplifying x + -18 = 20.784609691 Reorder the terms: -18 + x = 20.784609691 Solving -18 + x = 20.784609691 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 = 20.784609691 + 18 Combine like terms: -18 + 18 = 0 0 + x = 20.784609691 + 18 x = 20.784609691 + 18 Combine like terms: 20.784609691 + 18 = 38.784609691 x = 38.784609691 Simplifying x = 38.784609691Subproblem 2
x + -18 = -20.784609691 Simplifying x + -18 = -20.784609691 Reorder the terms: -18 + x = -20.784609691 Solving -18 + x = -20.784609691 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 = -20.784609691 + 18 Combine like terms: -18 + 18 = 0 0 + x = -20.784609691 + 18 x = -20.784609691 + 18 Combine like terms: -20.784609691 + 18 = -2.784609691 x = -2.784609691 Simplifying x = -2.784609691Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.784609691, -2.784609691}
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