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Simplifying x2 + -36x + -210 = 0 Reorder the terms: -210 + -36x + x2 = 0 Solving -210 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + -36x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + -36x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + -36x + x2 = 0 + 210 -36x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 -36x + x2 = 210 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 = 210 + 324 Reorder the terms: 324 + -36x + x2 = 210 + 324 Combine like terms: 210 + 324 = 534 324 + -36x + x2 = 534 Factor a perfect square on the left side: (x + -18)(x + -18) = 534 Calculate the square root of the right side: 23.108440017 Break this problem into two subproblems by setting (x + -18) equal to 23.108440017 and -23.108440017.Subproblem 1
x + -18 = 23.108440017 Simplifying x + -18 = 23.108440017 Reorder the terms: -18 + x = 23.108440017 Solving -18 + x = 23.108440017 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 = 23.108440017 + 18 Combine like terms: -18 + 18 = 0 0 + x = 23.108440017 + 18 x = 23.108440017 + 18 Combine like terms: 23.108440017 + 18 = 41.108440017 x = 41.108440017 Simplifying x = 41.108440017Subproblem 2
x + -18 = -23.108440017 Simplifying x + -18 = -23.108440017 Reorder the terms: -18 + x = -23.108440017 Solving -18 + x = -23.108440017 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 = -23.108440017 + 18 Combine like terms: -18 + 18 = 0 0 + x = -23.108440017 + 18 x = -23.108440017 + 18 Combine like terms: -23.108440017 + 18 = -5.108440017 x = -5.108440017 Simplifying x = -5.108440017Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.108440017, -5.108440017}
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