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Simplifying (-1x + -9i)(x + 9i) = 0 Reorder the terms: (-9i + -1x)(x + 9i) = 0 Reorder the terms: (-9i + -1x)(9i + x) = 0 Multiply (-9i + -1x) * (9i + x) (-9i * (9i + x) + -1x * (9i + x)) = 0 ((9i * -9i + x * -9i) + -1x * (9i + x)) = 0 Reorder the terms: ((-9ix + -81i2) + -1x * (9i + x)) = 0 ((-9ix + -81i2) + -1x * (9i + x)) = 0 (-9ix + -81i2 + (9i * -1x + x * -1x)) = 0 (-9ix + -81i2 + (-9ix + -1x2)) = 0 Reorder the terms: (-9ix + -9ix + -81i2 + -1x2) = 0 Combine like terms: -9ix + -9ix = -18ix (-18ix + -81i2 + -1x2) = 0 Solving -18ix + -81i2 + -1x2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(18ix + 81i2 + x2) = 0 Factor a trinomial. -1((9i + x)(9i + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9i + x)' equal to zero and attempt to solve: Simplifying 9i + x = 0 Solving 9i + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. 9i + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 9i + 0 = 0 + -1x 9i = 0 + -1x Remove the zero: 9i = -1x Divide each side by '9'. i = -0.1111111111x Simplifying i = -0.1111111111xSubproblem 2
Set the factor '(9i + x)' equal to zero and attempt to solve: Simplifying 9i + x = 0 Solving 9i + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. 9i + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 9i + 0 = 0 + -1x 9i = 0 + -1x Remove the zero: 9i = -1x Divide each side by '9'. i = -0.1111111111x Simplifying i = -0.1111111111xSolution
i = {-0.1111111111x, -0.1111111111x}
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