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Simplifying x2 + -1000x + 7.936 = 0 Reorder the terms: 7.936 + -1000x + x2 = 0 Solving 7.936 + -1000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7.936' to each side of the equation. 7.936 + -1000x + -7.936 + x2 = 0 + -7.936 Reorder the terms: 7.936 + -7.936 + -1000x + x2 = 0 + -7.936 Combine like terms: 7.936 + -7.936 = 0.000 0.000 + -1000x + x2 = 0 + -7.936 -1000x + x2 = 0 + -7.936 Combine like terms: 0 + -7.936 = -7.936 -1000x + x2 = -7.936 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = -7.936 + 250000 Reorder the terms: 250000 + -1000x + x2 = -7.936 + 250000 Combine like terms: -7.936 + 250000 = 249992.064 250000 + -1000x + x2 = 249992.064 Factor a perfect square on the left side: (x + -500)(x + -500) = 249992.064 Calculate the square root of the right side: 499.992063937 Break this problem into two subproblems by setting (x + -500) equal to 499.992063937 and -499.992063937.Subproblem 1
x + -500 = 499.992063937 Simplifying x + -500 = 499.992063937 Reorder the terms: -500 + x = 499.992063937 Solving -500 + x = 499.992063937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 499.992063937 + 500 Combine like terms: -500 + 500 = 0 0 + x = 499.992063937 + 500 x = 499.992063937 + 500 Combine like terms: 499.992063937 + 500 = 999.992063937 x = 999.992063937 Simplifying x = 999.992063937Subproblem 2
x + -500 = -499.992063937 Simplifying x + -500 = -499.992063937 Reorder the terms: -500 + x = -499.992063937 Solving -500 + x = -499.992063937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -499.992063937 + 500 Combine like terms: -500 + 500 = 0 0 + x = -499.992063937 + 500 x = -499.992063937 + 500 Combine like terms: -499.992063937 + 500 = 0.007936063 x = 0.007936063 Simplifying x = 0.007936063Solution
The solution to the problem is based on the solutions from the subproblems. x = {999.992063937, 0.007936063}
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