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Simplifying 2x2 + -1x + -252 = 0 Reorder the terms: -252 + -1x + 2x2 = 0 Solving -252 + -1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -126 + -0.5x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + -0.5x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + -0.5x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -0.5x + x2 = 0 + 126 -0.5x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 -0.5x + x2 = 126 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 126 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 126 + 0.0625 Combine like terms: 126 + 0.0625 = 126.0625 0.0625 + -0.5x + x2 = 126.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 126.0625 Calculate the square root of the right side: 11.227755786 Break this problem into two subproblems by setting (x + -0.25) equal to 11.227755786 and -11.227755786.Subproblem 1
x + -0.25 = 11.227755786 Simplifying x + -0.25 = 11.227755786 Reorder the terms: -0.25 + x = 11.227755786 Solving -0.25 + x = 11.227755786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 11.227755786 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 11.227755786 + 0.25 x = 11.227755786 + 0.25 Combine like terms: 11.227755786 + 0.25 = 11.477755786 x = 11.477755786 Simplifying x = 11.477755786Subproblem 2
x + -0.25 = -11.227755786 Simplifying x + -0.25 = -11.227755786 Reorder the terms: -0.25 + x = -11.227755786 Solving -0.25 + x = -11.227755786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -11.227755786 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -11.227755786 + 0.25 x = -11.227755786 + 0.25 Combine like terms: -11.227755786 + 0.25 = -10.977755786 x = -10.977755786 Simplifying x = -10.977755786Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.477755786, -10.977755786}
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