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Simplifying x2 + -52x + -231 = 0 Reorder the terms: -231 + -52x + x2 = 0 Solving -231 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '231' to each side of the equation. -231 + -52x + 231 + x2 = 0 + 231 Reorder the terms: -231 + 231 + -52x + x2 = 0 + 231 Combine like terms: -231 + 231 = 0 0 + -52x + x2 = 0 + 231 -52x + x2 = 0 + 231 Combine like terms: 0 + 231 = 231 -52x + x2 = 231 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = 231 + 676 Reorder the terms: 676 + -52x + x2 = 231 + 676 Combine like terms: 231 + 676 = 907 676 + -52x + x2 = 907 Factor a perfect square on the left side: (x + -26)(x + -26) = 907 Calculate the square root of the right side: 30.116440693 Break this problem into two subproblems by setting (x + -26) equal to 30.116440693 and -30.116440693.Subproblem 1
x + -26 = 30.116440693 Simplifying x + -26 = 30.116440693 Reorder the terms: -26 + x = 30.116440693 Solving -26 + x = 30.116440693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 30.116440693 + 26 Combine like terms: -26 + 26 = 0 0 + x = 30.116440693 + 26 x = 30.116440693 + 26 Combine like terms: 30.116440693 + 26 = 56.116440693 x = 56.116440693 Simplifying x = 56.116440693Subproblem 2
x + -26 = -30.116440693 Simplifying x + -26 = -30.116440693 Reorder the terms: -26 + x = -30.116440693 Solving -26 + x = -30.116440693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -30.116440693 + 26 Combine like terms: -26 + 26 = 0 0 + x = -30.116440693 + 26 x = -30.116440693 + 26 Combine like terms: -30.116440693 + 26 = -4.116440693 x = -4.116440693 Simplifying x = -4.116440693Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.116440693, -4.116440693}
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