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Simplifying x2 + -36x + -140 = 0 Reorder the terms: -140 + -36x + x2 = 0 Solving -140 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -36x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -36x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -36x + x2 = 0 + 140 -36x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -36x + x2 = 140 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 = 140 + 324 Reorder the terms: 324 + -36x + x2 = 140 + 324 Combine like terms: 140 + 324 = 464 324 + -36x + x2 = 464 Factor a perfect square on the left side: (x + -18)(x + -18) = 464 Calculate the square root of the right side: 21.540659229 Break this problem into two subproblems by setting (x + -18) equal to 21.540659229 and -21.540659229.Subproblem 1
x + -18 = 21.540659229 Simplifying x + -18 = 21.540659229 Reorder the terms: -18 + x = 21.540659229 Solving -18 + x = 21.540659229 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 = 21.540659229 + 18 Combine like terms: -18 + 18 = 0 0 + x = 21.540659229 + 18 x = 21.540659229 + 18 Combine like terms: 21.540659229 + 18 = 39.540659229 x = 39.540659229 Simplifying x = 39.540659229Subproblem 2
x + -18 = -21.540659229 Simplifying x + -18 = -21.540659229 Reorder the terms: -18 + x = -21.540659229 Solving -18 + x = -21.540659229 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 = -21.540659229 + 18 Combine like terms: -18 + 18 = 0 0 + x = -21.540659229 + 18 x = -21.540659229 + 18 Combine like terms: -21.540659229 + 18 = -3.540659229 x = -3.540659229 Simplifying x = -3.540659229Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.540659229, -3.540659229}
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