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Simplifying (x * x) + x + -200 = 0 Multiply x * x (x2) + x + -200 = 0 x2 + x + -200 = 0 Reorder the terms: -200 + x + x2 = 0 Solving -200 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + x + x2 = 0 + 200 x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 x + x2 = 200 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 = 200 + 0.25 Reorder the terms: 0.25 + x + x2 = 200 + 0.25 Combine like terms: 200 + 0.25 = 200.25 0.25 + x + x2 = 200.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 0.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 0.5 = 14.150971698 Simplifying x + 0.5 = 14.150971698 Reorder the terms: 0.5 + x = 14.150971698 Solving 0.5 + x = 14.150971698 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 = 14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.150971698 + -0.5 x = 14.150971698 + -0.5 Combine like terms: 14.150971698 + -0.5 = 13.650971698 x = 13.650971698 Simplifying x = 13.650971698Subproblem 2
x + 0.5 = -14.150971698 Simplifying x + 0.5 = -14.150971698 Reorder the terms: 0.5 + x = -14.150971698 Solving 0.5 + x = -14.150971698 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 = -14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.150971698 + -0.5 x = -14.150971698 + -0.5 Combine like terms: -14.150971698 + -0.5 = -14.650971698 x = -14.650971698 Simplifying x = -14.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.650971698, -14.650971698}
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