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Simplifying x2 + -36x + 322 = 0 Reorder the terms: 322 + -36x + x2 = 0 Solving 322 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-322' to each side of the equation. 322 + -36x + -322 + x2 = 0 + -322 Reorder the terms: 322 + -322 + -36x + x2 = 0 + -322 Combine like terms: 322 + -322 = 0 0 + -36x + x2 = 0 + -322 -36x + x2 = 0 + -322 Combine like terms: 0 + -322 = -322 -36x + x2 = -322 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 = -322 + 324 Reorder the terms: 324 + -36x + x2 = -322 + 324 Combine like terms: -322 + 324 = 2 324 + -36x + x2 = 2 Factor a perfect square on the left side: (x + -18)(x + -18) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -18) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -18 = 1.414213562 Simplifying x + -18 = 1.414213562 Reorder the terms: -18 + x = 1.414213562 Solving -18 + x = 1.414213562 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 = 1.414213562 + 18 Combine like terms: -18 + 18 = 0 0 + x = 1.414213562 + 18 x = 1.414213562 + 18 Combine like terms: 1.414213562 + 18 = 19.414213562 x = 19.414213562 Simplifying x = 19.414213562Subproblem 2
x + -18 = -1.414213562 Simplifying x + -18 = -1.414213562 Reorder the terms: -18 + x = -1.414213562 Solving -18 + x = -1.414213562 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 = -1.414213562 + 18 Combine like terms: -18 + 18 = 0 0 + x = -1.414213562 + 18 x = -1.414213562 + 18 Combine like terms: -1.414213562 + 18 = 16.585786438 x = 16.585786438 Simplifying x = 16.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.414213562, 16.585786438}
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