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Simplifying 2x4 + -2ix2 + -4i2 = 0 Reorder the terms: -2ix2 + -4i2 + 2x4 = 0 Solving -2ix2 + -4i2 + 2x4 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1ix2 + -2i2 + x4) = 0 Factor a trinomial. 2((-1i + -1x2)(2i + -1x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1i + -1x2)' equal to zero and attempt to solve: Simplifying -1i + -1x2 = 0 Solving -1i + -1x2 = 0 Move all terms containing i to the left, all other terms to the right. Add 'x2' to each side of the equation. -1i + -1x2 + x2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 -1i + 0 = 0 + x2 -1i = 0 + x2 Remove the zero: -1i = x2 Divide each side by '-1'. i = -1x2 Simplifying i = -1x2Subproblem 2
Set the factor '(2i + -1x2)' equal to zero and attempt to solve: Simplifying 2i + -1x2 = 0 Solving 2i + -1x2 = 0 Move all terms containing i to the left, all other terms to the right. Add 'x2' to each side of the equation. 2i + -1x2 + x2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 2i + 0 = 0 + x2 2i = 0 + x2 Remove the zero: 2i = x2 Divide each side by '2'. i = 0.5x2 Simplifying i = 0.5x2Solution
i = {-1x2, 0.5x2}
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