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Simplifying x4 + 11x2 + 26 = 0 Reorder the terms: 26 + 11x2 + x4 = 0 Solving 26 + 11x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 11x2 + -26 + x4 = 0 + -26 Reorder the terms: 26 + -26 + 11x2 + x4 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 11x2 + x4 = 0 + -26 11x2 + x4 = 0 + -26 Combine like terms: 0 + -26 = -26 11x2 + x4 = -26 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 = -26 + 30.25 Reorder the terms: 30.25 + 11x2 + x4 = -26 + 30.25 Combine like terms: -26 + 30.25 = 4.25 30.25 + 11x2 + x4 = 4.25 Factor a perfect square on the left side: (x2 + 5.5)(x2 + 5.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x2 + 5.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x2 + 5.5 = 2.061552813 Simplifying x2 + 5.5 = 2.061552813 Reorder the terms: 5.5 + x2 = 2.061552813 Solving 5.5 + x2 = 2.061552813 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 = 2.061552813 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = 2.061552813 + -5.5 x2 = 2.061552813 + -5.5 Combine like terms: 2.061552813 + -5.5 = -3.438447187 x2 = -3.438447187 Simplifying x2 = -3.438447187 Reorder the terms: 3.438447187 + x2 = -3.438447187 + 3.438447187 Combine like terms: -3.438447187 + 3.438447187 = 0.000000000 3.438447187 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 5.5 = -2.061552813 Simplifying x2 + 5.5 = -2.061552813 Reorder the terms: 5.5 + x2 = -2.061552813 Solving 5.5 + x2 = -2.061552813 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 = -2.061552813 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = -2.061552813 + -5.5 x2 = -2.061552813 + -5.5 Combine like terms: -2.061552813 + -5.5 = -7.561552813 x2 = -7.561552813 Simplifying x2 = -7.561552813 Reorder the terms: 7.561552813 + x2 = -7.561552813 + 7.561552813 Combine like terms: -7.561552813 + 7.561552813 = 0.000000000 7.561552813 + 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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