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Simplifying x4 + -22x2 + -50 = 0 Reorder the terms: -50 + -22x2 + x4 = 0 Solving -50 + -22x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -22x2 + 50 + x4 = 0 + 50 Reorder the terms: -50 + 50 + -22x2 + x4 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -22x2 + x4 = 0 + 50 -22x2 + x4 = 0 + 50 Combine like terms: 0 + 50 = 50 -22x2 + x4 = 50 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 = 50 + 121 Reorder the terms: 121 + -22x2 + x4 = 50 + 121 Combine like terms: 50 + 121 = 171 121 + -22x2 + x4 = 171 Factor a perfect square on the left side: (x2 + -11)(x2 + -11) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x2 + -11) equal to 13.076696831 and -13.076696831.Subproblem 1
x2 + -11 = 13.076696831 Simplifying x2 + -11 = 13.076696831 Reorder the terms: -11 + x2 = 13.076696831 Solving -11 + x2 = 13.076696831 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 = 13.076696831 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = 13.076696831 + 11 x2 = 13.076696831 + 11 Combine like terms: 13.076696831 + 11 = 24.076696831 x2 = 24.076696831 Simplifying x2 = 24.076696831 Take the square root of each side: x = {-4.906801079, 4.906801079}Subproblem 2
x2 + -11 = -13.076696831 Simplifying x2 + -11 = -13.076696831 Reorder the terms: -11 + x2 = -13.076696831 Solving -11 + x2 = -13.076696831 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 = -13.076696831 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = -13.076696831 + 11 x2 = -13.076696831 + 11 Combine like terms: -13.076696831 + 11 = -2.076696831 x2 = -2.076696831 Simplifying x2 = -2.076696831 Reorder the terms: 2.076696831 + x2 = -2.076696831 + 2.076696831 Combine like terms: -2.076696831 + 2.076696831 = 0.000000000 2.076696831 + 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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