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Simplifying x4 + -11x2 + -1 = 0 Reorder the terms: -1 + -11x2 + x4 = 0 Solving -1 + -11x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -11x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -11x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -11x2 + x4 = 0 + 1 -11x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -11x2 + x4 = 1 The x term is -11x2. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x2 + 30.25 + x4 = 1 + 30.25 Reorder the terms: 30.25 + -11x2 + x4 = 1 + 30.25 Combine like terms: 1 + 30.25 = 31.25 30.25 + -11x2 + x4 = 31.25 Factor a perfect square on the left side: (x2 + -5.5)(x2 + -5.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x2 + -5.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x2 + -5.5 = 5.590169944 Simplifying x2 + -5.5 = 5.590169944 Reorder the terms: -5.5 + x2 = 5.590169944 Solving -5.5 + x2 = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = 5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = 5.590169944 + 5.5 x2 = 5.590169944 + 5.5 Combine like terms: 5.590169944 + 5.5 = 11.090169944 x2 = 11.090169944 Simplifying x2 = 11.090169944 Take the square root of each side: x = {-3.330190677, 3.330190677}Subproblem 2
x2 + -5.5 = -5.590169944 Simplifying x2 + -5.5 = -5.590169944 Reorder the terms: -5.5 + x2 = -5.590169944 Solving -5.5 + x2 = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = -5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = -5.590169944 + 5.5 x2 = -5.590169944 + 5.5 Combine like terms: -5.590169944 + 5.5 = -0.090169944 x2 = -0.090169944 Simplifying x2 = -0.090169944 Reorder the terms: 0.090169944 + x2 = -0.090169944 + 0.090169944 Combine like terms: -0.090169944 + 0.090169944 = 0.000000000 0.090169944 + 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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