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Simplifying 300i2 + -2700i = -5400 Reorder the terms: -2700i + 300i2 = -5400 Solving -2700i + 300i2 = -5400 Solving for variable 'i'. Reorder the terms: 5400 + -2700i + 300i2 = -5400 + 5400 Combine like terms: -5400 + 5400 = 0 5400 + -2700i + 300i2 = 0 Factor out the Greatest Common Factor (GCF), '300'. 300(18 + -9i + i2) = 0 Factor a trinomial. 300((3 + -1i)(6 + -1i)) = 0 Ignore the factor 300.Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Subproblem 2
Set the factor '(6 + -1i)' equal to zero and attempt to solve: Simplifying 6 + -1i = 0 Solving 6 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1i = 0 + -6 -1i = 0 + -6 Combine like terms: 0 + -6 = -6 -1i = -6 Divide each side by '-1'. i = 6 Simplifying i = 6Solution
i = {3, 6}
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