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Simplifying x2 + -36x + -125 = 0 Reorder the terms: -125 + -36x + x2 = 0 Solving -125 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -36x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -36x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -36x + x2 = 0 + 125 -36x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -36x + x2 = 125 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 = 125 + 324 Reorder the terms: 324 + -36x + x2 = 125 + 324 Combine like terms: 125 + 324 = 449 324 + -36x + x2 = 449 Factor a perfect square on the left side: (x + -18)(x + -18) = 449 Calculate the square root of the right side: 21.1896201 Break this problem into two subproblems by setting (x + -18) equal to 21.1896201 and -21.1896201.Subproblem 1
x + -18 = 21.1896201 Simplifying x + -18 = 21.1896201 Reorder the terms: -18 + x = 21.1896201 Solving -18 + x = 21.1896201 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 = 21.1896201 + 18 Combine like terms: -18 + 18 = 0 0 + x = 21.1896201 + 18 x = 21.1896201 + 18 Combine like terms: 21.1896201 + 18 = 39.1896201 x = 39.1896201 Simplifying x = 39.1896201Subproblem 2
x + -18 = -21.1896201 Simplifying x + -18 = -21.1896201 Reorder the terms: -18 + x = -21.1896201 Solving -18 + x = -21.1896201 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 = -21.1896201 + 18 Combine like terms: -18 + 18 = 0 0 + x = -21.1896201 + 18 x = -21.1896201 + 18 Combine like terms: -21.1896201 + 18 = -3.1896201 x = -3.1896201 Simplifying x = -3.1896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.1896201, -3.1896201}
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