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Simplifying x4 + -22x2 + -45 = 0 Reorder the terms: -45 + -22x2 + x4 = 0 Solving -45 + -22x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -22x2 + 45 + x4 = 0 + 45 Reorder the terms: -45 + 45 + -22x2 + x4 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -22x2 + x4 = 0 + 45 -22x2 + x4 = 0 + 45 Combine like terms: 0 + 45 = 45 -22x2 + x4 = 45 The x term is -22x2. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x2 + 121 + x4 = 45 + 121 Reorder the terms: 121 + -22x2 + x4 = 45 + 121 Combine like terms: 45 + 121 = 166 121 + -22x2 + x4 = 166 Factor a perfect square on the left side: (x2 + -11)(x2 + -11) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x2 + -11) equal to 12.884098727 and -12.884098727.Subproblem 1
x2 + -11 = 12.884098727 Simplifying x2 + -11 = 12.884098727 Reorder the terms: -11 + x2 = 12.884098727 Solving -11 + x2 = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x2 = 12.884098727 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = 12.884098727 + 11 x2 = 12.884098727 + 11 Combine like terms: 12.884098727 + 11 = 23.884098727 x2 = 23.884098727 Simplifying x2 = 23.884098727 Take the square root of each side: x = {-4.887136045, 4.887136045}Subproblem 2
x2 + -11 = -12.884098727 Simplifying x2 + -11 = -12.884098727 Reorder the terms: -11 + x2 = -12.884098727 Solving -11 + x2 = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x2 = -12.884098727 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = -12.884098727 + 11 x2 = -12.884098727 + 11 Combine like terms: -12.884098727 + 11 = -1.884098727 x2 = -1.884098727 Simplifying x2 = -1.884098727 Reorder the terms: 1.884098727 + x2 = -1.884098727 + 1.884098727 Combine like terms: -1.884098727 + 1.884098727 = 0.000000000 1.884098727 + 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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