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Simplifying (-5 + 5i)(-5 + -5i)(x + -3)(x + -3) = 0 Reorder the terms: (-5 + 5i)(-5 + -5i)(-3 + x)(x + -3) = 0 Reorder the terms: (-5 + 5i)(-5 + -5i)(-3 + x)(-3 + x) = 0 Multiply (-5 + 5i) * (-5 + -5i) (-5(-5 + -5i) + 5i * (-5 + -5i))(-3 + x)(-3 + x) = 0 ((-5 * -5 + -5i * -5) + 5i * (-5 + -5i))(-3 + x)(-3 + x) = 0 ((25 + 25i) + 5i * (-5 + -5i))(-3 + x)(-3 + x) = 0 (25 + 25i + (-5 * 5i + -5i * 5i))(-3 + x)(-3 + x) = 0 (25 + 25i + (-25i + -25i2))(-3 + x)(-3 + x) = 0 Combine like terms: 25i + -25i = 0 (25 + 0 + -25i2)(-3 + x)(-3 + x) = 0 (25 + -25i2)(-3 + x)(-3 + x) = 0 Multiply (25 + -25i2) * (-3 + x) (25(-3 + x) + -25i2 * (-3 + x))(-3 + x) = 0 ((-3 * 25 + x * 25) + -25i2 * (-3 + x))(-3 + x) = 0 ((-75 + 25x) + -25i2 * (-3 + x))(-3 + x) = 0 (-75 + 25x + (-3 * -25i2 + x * -25i2))(-3 + x) = 0 (-75 + 25x + (75i2 + -25i2x))(-3 + x) = 0 Reorder the terms: (-75 + 75i2 + -25i2x + 25x)(-3 + x) = 0 (-75 + 75i2 + -25i2x + 25x)(-3 + x) = 0 Multiply (-75 + 75i2 + -25i2x + 25x) * (-3 + x) (-75(-3 + x) + 75i2 * (-3 + x) + -25i2x * (-3 + x) + 25x * (-3 + x)) = 0 ((-3 * -75 + x * -75) + 75i2 * (-3 + x) + -25i2x * (-3 + x) + 25x * (-3 + x)) = 0 ((225 + -75x) + 75i2 * (-3 + x) + -25i2x * (-3 + x) + 25x * (-3 + x)) = 0 (225 + -75x + (-3 * 75i2 + x * 75i2) + -25i2x * (-3 + x) + 25x * (-3 + x)) = 0 (225 + -75x + (-225i2 + 75i2x) + -25i2x * (-3 + x) + 25x * (-3 + x)) = 0 (225 + -75x + -225i2 + 75i2x + (-3 * -25i2x + x * -25i2x) + 25x * (-3 + x)) = 0 (225 + -75x + -225i2 + 75i2x + (75i2x + -25i2x2) + 25x * (-3 + x)) = 0 (225 + -75x + -225i2 + 75i2x + 75i2x + -25i2x2 + (-3 * 25x + x * 25x)) = 0 (225 + -75x + -225i2 + 75i2x + 75i2x + -25i2x2 + (-75x + 25x2)) = 0 Reorder the terms: (225 + -225i2 + 75i2x + 75i2x + -25i2x2 + -75x + -75x + 25x2) = 0 Combine like terms: 75i2x + 75i2x = 150i2x (225 + -225i2 + 150i2x + -25i2x2 + -75x + -75x + 25x2) = 0 Combine like terms: -75x + -75x = -150x (225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2) = 0 Solving 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-225' to each side of the equation. 225 + -225i2 + 150i2x + -25i2x2 + -150x + -225 + 25x2 = 0 + -225 Reorder the terms: 225 + -225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 + -225 -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = -225 Add '150x' to each side of the equation. -225i2 + 150i2x + -25i2x2 + -150x + 150x + 25x2 = -225 + 150x Combine like terms: -150x + 150x = 0 -225i2 + 150i2x + -25i2x2 + 0 + 25x2 = -225 + 150x -225i2 + 150i2x + -25i2x2 + 25x2 = -225 + 150x Add '-25x2' to each side of the equation. -225i2 + 150i2x + -25i2x2 + 25x2 + -25x2 = -225 + 150x + -25x2 Combine like terms: 25x2 + -25x2 = 0 -225i2 + 150i2x + -25i2x2 + 0 = -225 + 150x + -25x2 -225i2 + 150i2x + -25i2x2 = -225 + 150x + -25x2 Reorder the terms: 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = -225 + 150x + -25x2 + 225 + -150x + 25x2 Reorder the terms: 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = -225 + 225 + 150x + -150x + -25x2 + 25x2 Combine like terms: -225 + 225 = 0 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 + 150x + -150x + -25x2 + 25x2 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 150x + -150x + -25x2 + 25x2 Combine like terms: 150x + -150x = 0 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 + -25x2 + 25x2 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 225 + -225i2 + 150i2x + -25i2x2 + -150x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(9 + -9i2 + 6i2x + -1i2x2 + -6x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(9 + -9i2 + 6i2x + -1i2x2 + -6x + x2)' equal to zero and attempt to solve: Simplifying 9 + -9i2 + 6i2x + -1i2x2 + -6x + x2 = 0 Solving 9 + -9i2 + 6i2x + -1i2x2 + -6x + x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9i2 + 6i2x + -1i2x2 + -6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -9i2 + 6i2x + -1i2x2 + -6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9i2 + 6i2x + -1i2x2 + -6x + x2 = 0 + -9 -9i2 + 6i2x + -1i2x2 + -6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9i2 + 6i2x + -1i2x2 + -6x + x2 = -9 Add '6x' to each side of the equation. -9i2 + 6i2x + -1i2x2 + -6x + 6x + x2 = -9 + 6x Combine like terms: -6x + 6x = 0 -9i2 + 6i2x + -1i2x2 + 0 + x2 = -9 + 6x -9i2 + 6i2x + -1i2x2 + x2 = -9 + 6x Add '-1x2' to each side of the equation. -9i2 + 6i2x + -1i2x2 + x2 + -1x2 = -9 + 6x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 6i2x + -1i2x2 + 0 = -9 + 6x + -1x2 -9i2 + 6i2x + -1i2x2 = -9 + 6x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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