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Simplifying x4 + -11x2 + -112 = 0 Reorder the terms: -112 + -11x2 + x4 = 0 Solving -112 + -11x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -11x2 + 112 + x4 = 0 + 112 Reorder the terms: -112 + 112 + -11x2 + x4 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -11x2 + x4 = 0 + 112 -11x2 + x4 = 0 + 112 Combine like terms: 0 + 112 = 112 -11x2 + x4 = 112 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 = 112 + 30.25 Reorder the terms: 30.25 + -11x2 + x4 = 112 + 30.25 Combine like terms: 112 + 30.25 = 142.25 30.25 + -11x2 + x4 = 142.25 Factor a perfect square on the left side: (x2 + -5.5)(x2 + -5.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x2 + -5.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x2 + -5.5 = 11.926860442 Simplifying x2 + -5.5 = 11.926860442 Reorder the terms: -5.5 + x2 = 11.926860442 Solving -5.5 + x2 = 11.926860442 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 = 11.926860442 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = 11.926860442 + 5.5 x2 = 11.926860442 + 5.5 Combine like terms: 11.926860442 + 5.5 = 17.426860442 x2 = 17.426860442 Simplifying x2 = 17.426860442 Take the square root of each side: x = {-4.17454913, 4.17454913}Subproblem 2
x2 + -5.5 = -11.926860442 Simplifying x2 + -5.5 = -11.926860442 Reorder the terms: -5.5 + x2 = -11.926860442 Solving -5.5 + x2 = -11.926860442 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 = -11.926860442 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = -11.926860442 + 5.5 x2 = -11.926860442 + 5.5 Combine like terms: -11.926860442 + 5.5 = -6.426860442 x2 = -6.426860442 Simplifying x2 = -6.426860442 Reorder the terms: 6.426860442 + x2 = -6.426860442 + 6.426860442 Combine like terms: -6.426860442 + 6.426860442 = 0.000000000 6.426860442 + 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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