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Simplifying x2 + -36x + -20 = 0 Reorder the terms: -20 + -36x + x2 = 0 Solving -20 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -36x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -36x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -36x + x2 = 0 + 20 -36x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -36x + x2 = 20 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 = 20 + 324 Reorder the terms: 324 + -36x + x2 = 20 + 324 Combine like terms: 20 + 324 = 344 324 + -36x + x2 = 344 Factor a perfect square on the left side: (x + -18)(x + -18) = 344 Calculate the square root of the right side: 18.547236991 Break this problem into two subproblems by setting (x + -18) equal to 18.547236991 and -18.547236991.Subproblem 1
x + -18 = 18.547236991 Simplifying x + -18 = 18.547236991 Reorder the terms: -18 + x = 18.547236991 Solving -18 + x = 18.547236991 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 = 18.547236991 + 18 Combine like terms: -18 + 18 = 0 0 + x = 18.547236991 + 18 x = 18.547236991 + 18 Combine like terms: 18.547236991 + 18 = 36.547236991 x = 36.547236991 Simplifying x = 36.547236991Subproblem 2
x + -18 = -18.547236991 Simplifying x + -18 = -18.547236991 Reorder the terms: -18 + x = -18.547236991 Solving -18 + x = -18.547236991 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 = -18.547236991 + 18 Combine like terms: -18 + 18 = 0 0 + x = -18.547236991 + 18 x = -18.547236991 + 18 Combine like terms: -18.547236991 + 18 = -0.547236991 x = -0.547236991 Simplifying x = -0.547236991Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.547236991, -0.547236991}
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