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Simplifying (x * x + -1000) + (2x + -1000) + (2x + -1000) = 0 Multiply x * x (x2 + -1000) + (2x + -1000) + (2x + -1000) = 0 Reorder the terms: (-1000 + x2) + (2x + -1000) + (2x + -1000) = 0 Remove parenthesis around (-1000 + x2) -1000 + x2 + (2x + -1000) + (2x + -1000) = 0 Reorder the terms: -1000 + x2 + (-1000 + 2x) + (2x + -1000) = 0 Remove parenthesis around (-1000 + 2x) -1000 + x2 + -1000 + 2x + (2x + -1000) = 0 Reorder the terms: -1000 + x2 + -1000 + 2x + (-1000 + 2x) = 0 Remove parenthesis around (-1000 + 2x) -1000 + x2 + -1000 + 2x + -1000 + 2x = 0 Reorder the terms: -1000 + -1000 + -1000 + 2x + 2x + x2 = 0 Combine like terms: -1000 + -1000 = -2000 -2000 + -1000 + 2x + 2x + x2 = 0 Combine like terms: -2000 + -1000 = -3000 -3000 + 2x + 2x + x2 = 0 Combine like terms: 2x + 2x = 4x -3000 + 4x + x2 = 0 Solving -3000 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 4x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 4x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 4x + x2 = 0 + 3000 4x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 4x + x2 = 3000 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3000 + 4 Reorder the terms: 4 + 4x + x2 = 3000 + 4 Combine like terms: 3000 + 4 = 3004 4 + 4x + x2 = 3004 Factor a perfect square on the left side: (x + 2)(x + 2) = 3004 Calculate the square root of the right side: 54.808758424 Break this problem into two subproblems by setting (x + 2) equal to 54.808758424 and -54.808758424.Subproblem 1
x + 2 = 54.808758424 Simplifying x + 2 = 54.808758424 Reorder the terms: 2 + x = 54.808758424 Solving 2 + x = 54.808758424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 54.808758424 + -2 Combine like terms: 2 + -2 = 0 0 + x = 54.808758424 + -2 x = 54.808758424 + -2 Combine like terms: 54.808758424 + -2 = 52.808758424 x = 52.808758424 Simplifying x = 52.808758424Subproblem 2
x + 2 = -54.808758424 Simplifying x + 2 = -54.808758424 Reorder the terms: 2 + x = -54.808758424 Solving 2 + x = -54.808758424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -54.808758424 + -2 Combine like terms: 2 + -2 = 0 0 + x = -54.808758424 + -2 x = -54.808758424 + -2 Combine like terms: -54.808758424 + -2 = -56.808758424 x = -56.808758424 Simplifying x = -56.808758424Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.808758424, -56.808758424}
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