[tex]x\text{ = }3+2\text{i }\sqrt[]{6}\text{ or x = }3-2\text{i }\sqrt[]{6}[/tex]Explanation:[tex]x^2\text{ - 6x + 34 = 0}[/tex]
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} \text{where a = 1, b = -6, c = 34} \\ x\text{ = }\frac{-(-6)\text{ }\pm\sqrt[]{(-6)^2-4(1)(34)}}{2(1)} \\ x\text{ = }\frac{6\text{ }\pm\sqrt[]{36-132}}{2} \\ x\text{ = }\frac{6\pm\sqrt[]{-96}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = = }\frac{6\pm\sqrt[]{-1\times96}}{2} \\ In\text{ }comple\text{ }xnumber,-1=i^2 \\ x\text{ = = }\frac{6\pm\sqrt[]{i^2\times16\times6}}{2} \\ x\text{ = }\frac{6\pm4\text{ i }\sqrt[]{6}}{2}\text{ } \\ x\text{ = }\frac{2(3\pm2\text{ i }\sqrt[]{6})}{2}\text{ } \\ x\text{ = }3\pm2\text{ i }\sqrt[]{6} \end{gathered}[/tex][tex]x\text{ = }3+2\text{ i }\sqrt[]{6}\text{ or x = }3-2\text{ i }\sqrt[]{6}[/tex]
