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Simplifying x2 + -1x + -2 = 1000 Reorder the terms: -2 + -1x + x2 = 1000 Solving -2 + -1x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -2 + -1000 + -1x + x2 = 1000 + -1000 Combine like terms: -2 + -1000 = -1002 -1002 + -1x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1002 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1002' to each side of the equation. -1002 + -1x + 1002 + x2 = 0 + 1002 Reorder the terms: -1002 + 1002 + -1x + x2 = 0 + 1002 Combine like terms: -1002 + 1002 = 0 0 + -1x + x2 = 0 + 1002 -1x + x2 = 0 + 1002 Combine like terms: 0 + 1002 = 1002 -1x + x2 = 1002 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1002 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1002 + 0.25 Combine like terms: 1002 + 0.25 = 1002.25 0.25 + -1x + x2 = 1002.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1002.25 Calculate the square root of the right side: 31.658332237 Break this problem into two subproblems by setting (x + -0.5) equal to 31.658332237 and -31.658332237.Subproblem 1
x + -0.5 = 31.658332237 Simplifying x + -0.5 = 31.658332237 Reorder the terms: -0.5 + x = 31.658332237 Solving -0.5 + x = 31.658332237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 31.658332237 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 31.658332237 + 0.5 x = 31.658332237 + 0.5 Combine like terms: 31.658332237 + 0.5 = 32.158332237 x = 32.158332237 Simplifying x = 32.158332237Subproblem 2
x + -0.5 = -31.658332237 Simplifying x + -0.5 = -31.658332237 Reorder the terms: -0.5 + x = -31.658332237 Solving -0.5 + x = -31.658332237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -31.658332237 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -31.658332237 + 0.5 x = -31.658332237 + 0.5 Combine like terms: -31.658332237 + 0.5 = -31.158332237 x = -31.158332237 Simplifying x = -31.158332237Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.158332237, -31.158332237}
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