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Simplifying x4 + x2 + -199 = 0 Reorder the terms: -199 + x2 + x4 = 0 Solving -199 + x2 + x4 = 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 + x2 + 199 + x4 = 0 + 199 Reorder the terms: -199 + 199 + x2 + x4 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + x2 + x4 = 0 + 199 x2 + x4 = 0 + 199 Combine like terms: 0 + 199 = 199 x2 + x4 = 199 The x term is x2. 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. x2 + 0.25 + x4 = 199 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 199 + 0.25 Combine like terms: 199 + 0.25 = 199.25 0.25 + x2 + x4 = 199.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 199.25 Calculate the square root of the right side: 14.115594213 Break this problem into two subproblems by setting (x2 + 0.5) equal to 14.115594213 and -14.115594213.Subproblem 1
x2 + 0.5 = 14.115594213 Simplifying x2 + 0.5 = 14.115594213 Reorder the terms: 0.5 + x2 = 14.115594213 Solving 0.5 + x2 = 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 + x2 = 14.115594213 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 14.115594213 + -0.5 x2 = 14.115594213 + -0.5 Combine like terms: 14.115594213 + -0.5 = 13.615594213 x2 = 13.615594213 Simplifying x2 = 13.615594213 Take the square root of each side: x = {-3.689931465, 3.689931465}Subproblem 2
x2 + 0.5 = -14.115594213 Simplifying x2 + 0.5 = -14.115594213 Reorder the terms: 0.5 + x2 = -14.115594213 Solving 0.5 + x2 = -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 + x2 = -14.115594213 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -14.115594213 + -0.5 x2 = -14.115594213 + -0.5 Combine like terms: -14.115594213 + -0.5 = -14.615594213 x2 = -14.615594213 Simplifying x2 = -14.615594213 Reorder the terms: 14.615594213 + x2 = -14.615594213 + 14.615594213 Combine like terms: -14.615594213 + 14.615594213 = 0.000000000 14.615594213 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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