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Simplifying x2 + -500x + 1000 = 0 Reorder the terms: 1000 + -500x + x2 = 0 Solving 1000 + -500x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -500x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -500x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -500x + x2 = 0 + -1000 -500x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -500x + x2 = -1000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -1000 + 62500 Reorder the terms: 62500 + -500x + x2 = -1000 + 62500 Combine like terms: -1000 + 62500 = 61500 62500 + -500x + x2 = 61500 Factor a perfect square on the left side: (x + -250)(x + -250) = 61500 Calculate the square root of the right side: 247.991935353 Break this problem into two subproblems by setting (x + -250) equal to 247.991935353 and -247.991935353.Subproblem 1
x + -250 = 247.991935353 Simplifying x + -250 = 247.991935353 Reorder the terms: -250 + x = 247.991935353 Solving -250 + x = 247.991935353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 247.991935353 + 250 Combine like terms: -250 + 250 = 0 0 + x = 247.991935353 + 250 x = 247.991935353 + 250 Combine like terms: 247.991935353 + 250 = 497.991935353 x = 497.991935353 Simplifying x = 497.991935353Subproblem 2
x + -250 = -247.991935353 Simplifying x + -250 = -247.991935353 Reorder the terms: -250 + x = -247.991935353 Solving -250 + x = -247.991935353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -247.991935353 + 250 Combine like terms: -250 + 250 = 0 0 + x = -247.991935353 + 250 x = -247.991935353 + 250 Combine like terms: -247.991935353 + 250 = 2.008064647 x = 2.008064647 Simplifying x = 2.008064647Solution
The solution to the problem is based on the solutions from the subproblems. x = {497.991935353, 2.008064647}
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