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Simplifying x2 + -1000x + 1000 = 0 Reorder the terms: 1000 + -1000x + x2 = 0 Solving 1000 + -1000x + 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 + -1000x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -1000x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -1000x + x2 = 0 + -1000 -1000x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -1000x + x2 = -1000 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 = -1000 + 250000 Reorder the terms: 250000 + -1000x + x2 = -1000 + 250000 Combine like terms: -1000 + 250000 = 249000 250000 + -1000x + x2 = 249000 Factor a perfect square on the left side: (x + -500)(x + -500) = 249000 Calculate the square root of the right side: 498.998997995 Break this problem into two subproblems by setting (x + -500) equal to 498.998997995 and -498.998997995.Subproblem 1
x + -500 = 498.998997995 Simplifying x + -500 = 498.998997995 Reorder the terms: -500 + x = 498.998997995 Solving -500 + x = 498.998997995 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 = 498.998997995 + 500 Combine like terms: -500 + 500 = 0 0 + x = 498.998997995 + 500 x = 498.998997995 + 500 Combine like terms: 498.998997995 + 500 = 998.998997995 x = 998.998997995 Simplifying x = 998.998997995Subproblem 2
x + -500 = -498.998997995 Simplifying x + -500 = -498.998997995 Reorder the terms: -500 + x = -498.998997995 Solving -500 + x = -498.998997995 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 = -498.998997995 + 500 Combine like terms: -500 + 500 = 0 0 + x = -498.998997995 + 500 x = -498.998997995 + 500 Combine like terms: -498.998997995 + 500 = 1.001002005 x = 1.001002005 Simplifying x = 1.001002005Solution
The solution to the problem is based on the solutions from the subproblems. x = {998.998997995, 1.001002005}
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