Question

Use the “complete the square” method to solve the following problemx^2 + 3x + 11 = 0

Answer 1

`x^2+3x+11=0`
`((1)/(2)*3)^2=(+(3)/(2))^2`
`\begin{gathered} x^2+3x=-11 \\ x^2+3x+(+(3)/(2))^2=-11+(9)/(4) \\ \\ (x+(3)/(2))^2=-(35)/(4) \\ \\ x+(3)/(2)=\sqrt{(-35)/(4)} \\ \\ x+(3)/(2)=\pm(√(35))/(2)i \\ \\ x=(-3)/(2)\pm(√(35))/(2)i \end{gathered}`

The answers are

`x=(-3)/(2)+(i√(35))/(2),\text{ }x=(-3)/(2)-(i√(35))/(2)`