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Simplifying x2 + -52.977x + 500 = 0 Reorder the terms: 500 + -52.977x + x2 = 0 Solving 500 + -52.977x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -52.977x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -52.977x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -52.977x + x2 = 0 + -500 -52.977x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -52.977x + x2 = -500 The x term is -52.977x. Take half its coefficient (-26.4885). Square it (701.6406323) and add it to both sides. Add '701.6406323' to each side of the equation. -52.977x + 701.6406323 + x2 = -500 + 701.6406323 Reorder the terms: 701.6406323 + -52.977x + x2 = -500 + 701.6406323 Combine like terms: -500 + 701.6406323 = 201.6406323 701.6406323 + -52.977x + x2 = 201.6406323 Factor a perfect square on the left side: (x + -26.4885)(x + -26.4885) = 201.6406323 Calculate the square root of the right side: 14.200022264 Break this problem into two subproblems by setting (x + -26.4885) equal to 14.200022264 and -14.200022264.Subproblem 1
x + -26.4885 = 14.200022264 Simplifying x + -26.4885 = 14.200022264 Reorder the terms: -26.4885 + x = 14.200022264 Solving -26.4885 + x = 14.200022264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.4885' to each side of the equation. -26.4885 + 26.4885 + x = 14.200022264 + 26.4885 Combine like terms: -26.4885 + 26.4885 = 0.0000 0.0000 + x = 14.200022264 + 26.4885 x = 14.200022264 + 26.4885 Combine like terms: 14.200022264 + 26.4885 = 40.688522264 x = 40.688522264 Simplifying x = 40.688522264Subproblem 2
x + -26.4885 = -14.200022264 Simplifying x + -26.4885 = -14.200022264 Reorder the terms: -26.4885 + x = -14.200022264 Solving -26.4885 + x = -14.200022264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.4885' to each side of the equation. -26.4885 + 26.4885 + x = -14.200022264 + 26.4885 Combine like terms: -26.4885 + 26.4885 = 0.0000 0.0000 + x = -14.200022264 + 26.4885 x = -14.200022264 + 26.4885 Combine like terms: -14.200022264 + 26.4885 = 12.288477736 x = 12.288477736 Simplifying x = 12.288477736Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.688522264, 12.288477736}
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