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Simplifying x4 + -11x2 + -18 = 0 Reorder the terms: -18 + -11x2 + x4 = 0 Solving -18 + -11x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -11x2 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + -11x2 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -11x2 + x4 = 0 + 18 -11x2 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 -11x2 + x4 = 18 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 = 18 + 30.25 Reorder the terms: 30.25 + -11x2 + x4 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + -11x2 + x4 = 48.25 Factor a perfect square on the left side: (x2 + -5.5)(x2 + -5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x2 + -5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x2 + -5.5 = 6.946221995 Simplifying x2 + -5.5 = 6.946221995 Reorder the terms: -5.5 + x2 = 6.946221995 Solving -5.5 + x2 = 6.946221995 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 = 6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = 6.946221995 + 5.5 x2 = 6.946221995 + 5.5 Combine like terms: 6.946221995 + 5.5 = 12.446221995 x2 = 12.446221995 Simplifying x2 = 12.446221995 Take the square root of each side: x = {-3.52792035, 3.52792035}Subproblem 2
x2 + -5.5 = -6.946221995 Simplifying x2 + -5.5 = -6.946221995 Reorder the terms: -5.5 + x2 = -6.946221995 Solving -5.5 + x2 = -6.946221995 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 = -6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = -6.946221995 + 5.5 x2 = -6.946221995 + 5.5 Combine like terms: -6.946221995 + 5.5 = -1.446221995 x2 = -1.446221995 Simplifying x2 = -1.446221995 Reorder the terms: 1.446221995 + x2 = -1.446221995 + 1.446221995 Combine like terms: -1.446221995 + 1.446221995 = 0.000000000 1.446221995 + 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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