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Simplifying x4 + 22x2 + 52 = 0 Reorder the terms: 52 + 22x2 + x4 = 0 Solving 52 + 22x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 22x2 + -52 + x4 = 0 + -52 Reorder the terms: 52 + -52 + 22x2 + x4 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 22x2 + x4 = 0 + -52 22x2 + x4 = 0 + -52 Combine like terms: 0 + -52 = -52 22x2 + x4 = -52 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 = -52 + 121 Reorder the terms: 121 + 22x2 + x4 = -52 + 121 Combine like terms: -52 + 121 = 69 121 + 22x2 + x4 = 69 Factor a perfect square on the left side: (x2 + 11)(x2 + 11) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x2 + 11) equal to 8.306623863 and -8.306623863.Subproblem 1
x2 + 11 = 8.306623863 Simplifying x2 + 11 = 8.306623863 Reorder the terms: 11 + x2 = 8.306623863 Solving 11 + x2 = 8.306623863 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 = 8.306623863 + -11 Combine like terms: 11 + -11 = 0 0 + x2 = 8.306623863 + -11 x2 = 8.306623863 + -11 Combine like terms: 8.306623863 + -11 = -2.693376137 x2 = -2.693376137 Simplifying x2 = -2.693376137 Reorder the terms: 2.693376137 + x2 = -2.693376137 + 2.693376137 Combine like terms: -2.693376137 + 2.693376137 = 0.000000000 2.693376137 + 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 + 11 = -8.306623863 Simplifying x2 + 11 = -8.306623863 Reorder the terms: 11 + x2 = -8.306623863 Solving 11 + x2 = -8.306623863 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 = -8.306623863 + -11 Combine like terms: 11 + -11 = 0 0 + x2 = -8.306623863 + -11 x2 = -8.306623863 + -11 Combine like terms: -8.306623863 + -11 = -19.306623863 x2 = -19.306623863 Simplifying x2 = -19.306623863 Reorder the terms: 19.306623863 + x2 = -19.306623863 + 19.306623863 Combine like terms: -19.306623863 + 19.306623863 = 0.000000000 19.306623863 + 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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