(iii) 3z2−18z+50=03z^2 - 18z + 50 = 03z2−18z+50=0 Solution Divide both sides by 3:z2−6z+503=0Isolate the constant term:z2−6z=−503Add (−62)2=(−3)2=9 to both sides:z2−6z+9=−503+9(z−3)2=−503+273=−233Take square root:z−3=±−233=±i233=±i693z=3±i693\begin{aligned} & \boxed{\text{Divide both sides by 3:}} \\ \\ & z^2 - 6z + \frac{50}{3} = 0 \\ \\ & \boxed{\text{Isolate the constant term:}} \\ \\ & z^2 - 6z = -\frac{50}{3} \\ \\ & \boxed{\text{Add } \left(\frac{-6}{2}\right)^2 = (-3)^2 = 9 \text{ to both sides:}} \\ \\ & z^2 - 6z + 9 = -\frac{50}{3} + 9 \\ \\ & (z - 3)^2 = -\frac{50}{3} + \frac{27}{3} = -\frac{23}{3} \\ \\ & \boxed{\text{Take square root:}} \\ \\ & z - 3 = \pm \sqrt{-\frac{23}{3}} = \pm i\sqrt{\frac{23}{3}} = \pm \frac{i\sqrt{69}}{3} \\ \\ & z = 3 \pm \frac{i\sqrt{69}}{3} \end{aligned}Divide both sides by 3:z2−6z+350=0Isolate the constant term:z2−6z=−350Add (2−6)2=(−3)2=9 to both sides:z2−6z+9=−350+9(z−3)2=−350+327=−323Take square root:z−3=±−323=±i323=±3i69z=3±3i69