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Simplifying x2 + x = 200000 Reorder the terms: x + x2 = 200000 Solving x + x2 = 200000 Solving for variable 'x'. Reorder the terms: -200000 + x + x2 = 200000 + -200000 Combine like terms: 200000 + -200000 = 0 -200000 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200000' to each side of the equation. -200000 + x + 200000 + x2 = 0 + 200000 Reorder the terms: -200000 + 200000 + x + x2 = 0 + 200000 Combine like terms: -200000 + 200000 = 0 0 + x + x2 = 0 + 200000 x + x2 = 0 + 200000 Combine like terms: 0 + 200000 = 200000 x + x2 = 200000 The x term is x. 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. x + 0.25 + x2 = 200000 + 0.25 Reorder the terms: 0.25 + x + x2 = 200000 + 0.25 Combine like terms: 200000 + 0.25 = 200000.25 0.25 + x + x2 = 200000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 200000.25 Calculate the square root of the right side: 447.213875008 Break this problem into two subproblems by setting (x + 0.5) equal to 447.213875008 and -447.213875008.Subproblem 1
x + 0.5 = 447.213875008 Simplifying x + 0.5 = 447.213875008 Reorder the terms: 0.5 + x = 447.213875008 Solving 0.5 + x = 447.213875008 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 = 447.213875008 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 447.213875008 + -0.5 x = 447.213875008 + -0.5 Combine like terms: 447.213875008 + -0.5 = 446.713875008 x = 446.713875008 Simplifying x = 446.713875008Subproblem 2
x + 0.5 = -447.213875008 Simplifying x + 0.5 = -447.213875008 Reorder the terms: 0.5 + x = -447.213875008 Solving 0.5 + x = -447.213875008 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 = -447.213875008 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -447.213875008 + -0.5 x = -447.213875008 + -0.5 Combine like terms: -447.213875008 + -0.5 = -447.713875008 x = -447.713875008 Simplifying x = -447.713875008Solution
The solution to the problem is based on the solutions from the subproblems. x = {446.713875008, -447.713875008}
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