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Simplifying (x + 2i)(x + 2i) = 0 Reorder the terms: (2i + x)(x + 2i) = 0 Reorder the terms: (2i + x)(2i + x) = 0 Multiply (2i + x) * (2i + x) (2i * (2i + x) + x(2i + x)) = 0 ((2i * 2i + x * 2i) + x(2i + x)) = 0 Reorder the terms: ((2ix + 4i2) + x(2i + x)) = 0 ((2ix + 4i2) + x(2i + x)) = 0 (2ix + 4i2 + (2i * x + x * x)) = 0 (2ix + 4i2 + (2ix + x2)) = 0 Reorder the terms: (2ix + 2ix + 4i2 + x2) = 0 Combine like terms: 2ix + 2ix = 4ix (4ix + 4i2 + x2) = 0 Solving 4ix + 4i2 + x2 = 0 Solving for variable 'i'. Factor a trinomial. (2i + x)(2i + x) = 0Subproblem 1
Set the factor '(2i + x)' equal to zero and attempt to solve: Simplifying 2i + x = 0 Solving 2i + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. 2i + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 2i + 0 = 0 + -1x 2i = 0 + -1x Remove the zero: 2i = -1x Divide each side by '2'. i = -0.5x Simplifying i = -0.5xSubproblem 2
Set the factor '(2i + x)' equal to zero and attempt to solve: Simplifying 2i + x = 0 Solving 2i + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. 2i + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 2i + 0 = 0 + -1x 2i = 0 + -1x Remove the zero: 2i = -1x Divide each side by '2'. i = -0.5x Simplifying i = -0.5xSolution
i = {-0.5x, -0.5x}
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