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Simplifying x2 + 2x + -200000 = 0 Reorder the terms: -200000 + 2x + x2 = 0 Solving -200000 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200000' to each side of the equation. -200000 + 2x + 200000 + x2 = 0 + 200000 Reorder the terms: -200000 + 200000 + 2x + x2 = 0 + 200000 Combine like terms: -200000 + 200000 = 0 0 + 2x + x2 = 0 + 200000 2x + x2 = 0 + 200000 Combine like terms: 0 + 200000 = 200000 2x + x2 = 200000 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 200000 + 1 Reorder the terms: 1 + 2x + x2 = 200000 + 1 Combine like terms: 200000 + 1 = 200001 1 + 2x + x2 = 200001 Factor a perfect square on the left side: (x + 1)(x + 1) = 200001 Calculate the square root of the right side: 447.214713533 Break this problem into two subproblems by setting (x + 1) equal to 447.214713533 and -447.214713533.Subproblem 1
x + 1 = 447.214713533 Simplifying x + 1 = 447.214713533 Reorder the terms: 1 + x = 447.214713533 Solving 1 + x = 447.214713533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 447.214713533 + -1 Combine like terms: 1 + -1 = 0 0 + x = 447.214713533 + -1 x = 447.214713533 + -1 Combine like terms: 447.214713533 + -1 = 446.214713533 x = 446.214713533 Simplifying x = 446.214713533Subproblem 2
x + 1 = -447.214713533 Simplifying x + 1 = -447.214713533 Reorder the terms: 1 + x = -447.214713533 Solving 1 + x = -447.214713533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -447.214713533 + -1 Combine like terms: 1 + -1 = 0 0 + x = -447.214713533 + -1 x = -447.214713533 + -1 Combine like terms: -447.214713533 + -1 = -448.214713533 x = -448.214713533 Simplifying x = -448.214713533Solution
The solution to the problem is based on the solutions from the subproblems. x = {446.214713533, -448.214713533}
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