Question

Help! Solve the equation and show all work. Use Quadratic Formula

Answer 1

`x\text{ = }3+2\text{i }\sqrt[]{6}\text{ or x = }3-2\text{i }\sqrt[]{6}`Step-by-step explanation:
`x^2\text{ - 6x + 34 = 0}`

Using quadratic formula:

`x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`
`\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}`
`\begin{gathered} x\text{ = = }\frac{6\pm\sqrt[]{-1*96}}{2} \\ In\text{ }comple\text{ }xnumber,-1=i^2 \\ x\text{ = = }\frac{6\pm\sqrt[]{i^2*16*6}}{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}`
`x\text{ = }3+2\text{ i }\sqrt[]{6}\text{ or x = }3-2\text{ i }\sqrt[]{6}`