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Simplifying (x + -1(4i))(x + -1(4i)) = 0 Remove parenthesis around (4i) (x + -1 * 4i)(x + -1(4i)) = 0 Multiply -1 * 4 (x + -4i)(x + -1(4i)) = 0 Reorder the terms: (-4i + x)(x + -1(4i)) = 0 Remove parenthesis around (4i) (-4i + x)(x + -1 * 4i) = 0 Multiply -1 * 4 (-4i + x)(x + -4i) = 0 Reorder the terms: (-4i + x)(-4i + x) = 0 Multiply (-4i + x) * (-4i + x) (-4i * (-4i + x) + x(-4i + x)) = 0 ((-4i * -4i + x * -4i) + x(-4i + x)) = 0 Reorder the terms: ((-4ix + 16i2) + x(-4i + x)) = 0 ((-4ix + 16i2) + x(-4i + x)) = 0 (-4ix + 16i2 + (-4i * x + x * x)) = 0 (-4ix + 16i2 + (-4ix + x2)) = 0 Reorder the terms: (-4ix + -4ix + 16i2 + x2) = 0 Combine like terms: -4ix + -4ix = -8ix (-8ix + 16i2 + x2) = 0 Solving -8ix + 16i2 + x2 = 0 Solving for variable 'i'. Factor a trinomial. (4i + -1x)(4i + -1x) = 0Subproblem 1
Set the factor '(4i + -1x)' equal to zero and attempt to solve: Simplifying 4i + -1x = 0 Solving 4i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 4i + -1x + x = 0 + x Combine like terms: -1x + x = 0 4i + 0 = 0 + x 4i = 0 + x Remove the zero: 4i = x Divide each side by '4'. i = 0.25x Simplifying i = 0.25xSubproblem 2
Set the factor '(4i + -1x)' equal to zero and attempt to solve: Simplifying 4i + -1x = 0 Solving 4i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 4i + -1x + x = 0 + x Combine like terms: -1x + x = 0 4i + 0 = 0 + x 4i = 0 + x Remove the zero: 4i = x Divide each side by '4'. i = 0.25x Simplifying i = 0.25xSolution
i = {0.25x, 0.25x}
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