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Simplifying x4 + -16x2 + -48 = 0 Reorder the terms: -48 + -16x2 + x4 = 0 Solving -48 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -16x2 + 48 + x4 = 0 + 48 Reorder the terms: -48 + 48 + -16x2 + x4 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -16x2 + x4 = 0 + 48 -16x2 + x4 = 0 + 48 Combine like terms: 0 + 48 = 48 -16x2 + x4 = 48 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = 48 + 64 Reorder the terms: 64 + -16x2 + x4 = 48 + 64 Combine like terms: 48 + 64 = 112 64 + -16x2 + x4 = 112 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x2 + -8) equal to 10.583005244 and -10.583005244.Subproblem 1
x2 + -8 = 10.583005244 Simplifying x2 + -8 = 10.583005244 Reorder the terms: -8 + x2 = 10.583005244 Solving -8 + x2 = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 10.583005244 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 10.583005244 + 8 x2 = 10.583005244 + 8 Combine like terms: 10.583005244 + 8 = 18.583005244 x2 = 18.583005244 Simplifying x2 = 18.583005244 Take the square root of each side: x = {-4.310800998, 4.310800998}Subproblem 2
x2 + -8 = -10.583005244 Simplifying x2 + -8 = -10.583005244 Reorder the terms: -8 + x2 = -10.583005244 Solving -8 + x2 = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -10.583005244 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -10.583005244 + 8 x2 = -10.583005244 + 8 Combine like terms: -10.583005244 + 8 = -2.583005244 x2 = -2.583005244 Simplifying x2 = -2.583005244 Reorder the terms: 2.583005244 + x2 = -2.583005244 + 2.583005244 Combine like terms: -2.583005244 + 2.583005244 = 0.000000000 2.583005244 + 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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