Question

Solve the quadratic equation by completing the square. 3r^2 +4r+9=0

Answer 1

Answer:
`r=-(2)/(3) \pm (i√(23))/(3)`

Explanation:

`3r^2 +4r+9=0\\\\3\left(r^2 +(4)/(3) r \right)+9=0\\\\3\left(\left(r+(2)/(3) \right)^2 -(4)/(9) \right)+9=0\\\\3\left(r+(2)/(3) \right)^2 -(4)/(3)+9=0\\\\3\left(r+(2)/(3) \right)^2 =-(23)/(3)\\\\\left(r+(2)/(3) \right)^2 =-(23)/(9)\\\\r+(2)/(3)=\pm (i√(23))/(3)\\\\r=-(2)/(3) \pm (i√(23))/(3)`