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Simplifying x2 + -1x + -199 = 0 Reorder the terms: -199 + -1x + x2 = 0 Solving -199 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '199' to each side of the equation. -199 + -1x + 199 + x2 = 0 + 199 Reorder the terms: -199 + 199 + -1x + x2 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + -1x + x2 = 0 + 199 -1x + x2 = 0 + 199 Combine like terms: 0 + 199 = 199 -1x + x2 = 199 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 = 199 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 199 + 0.25 Combine like terms: 199 + 0.25 = 199.25 0.25 + -1x + x2 = 199.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 199.25 Calculate the square root of the right side: 14.115594213 Break this problem into two subproblems by setting (x + -0.5) equal to 14.115594213 and -14.115594213.Subproblem 1
x + -0.5 = 14.115594213 Simplifying x + -0.5 = 14.115594213 Reorder the terms: -0.5 + x = 14.115594213 Solving -0.5 + x = 14.115594213 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 = 14.115594213 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 14.115594213 + 0.5 x = 14.115594213 + 0.5 Combine like terms: 14.115594213 + 0.5 = 14.615594213 x = 14.615594213 Simplifying x = 14.615594213Subproblem 2
x + -0.5 = -14.115594213 Simplifying x + -0.5 = -14.115594213 Reorder the terms: -0.5 + x = -14.115594213 Solving -0.5 + x = -14.115594213 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 = -14.115594213 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -14.115594213 + 0.5 x = -14.115594213 + 0.5 Combine like terms: -14.115594213 + 0.5 = -13.615594213 x = -13.615594213 Simplifying x = -13.615594213Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.615594213, -13.615594213}
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