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Simplifying -48x4 + -128x2 + 256 = 0 Reorder the terms: 256 + -128x2 + -48x4 = 0 Solving 256 + -128x2 + -48x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(16 + -8x2 + -3x4) = 0 Factor a trinomial. 16((4 + -3x2)(4 + x2)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(4 + -3x2)' equal to zero and attempt to solve: Simplifying 4 + -3x2 = 0 Solving 4 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x2 = 0 + -4 -3x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x2 = -4 Divide each side by '-3'. x2 = 1.333333333 Simplifying x2 = 1.333333333 Take the square root of each side: x = {-1.154700538, 1.154700538}Subproblem 2
Set the factor '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {-1.154700538, 1.154700538}
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