Question

Solve by completing the square. Express answer in a simplified radical form when possible. When not possible, round to nearest hundredth.

x^2+6x+2=0

Answer 1

`{ \tt{ {x}^(2) + 6x + 2 = 0}} \\ { \tt{ {x}^(2) + 6x = - 2 }}`

- Add the square of the half of the sum on either sides:

`{ \tt{ {x}^(2) + 6x + ( { (6)/(2)) }^(2) = - 2 + {( (6)/(2)) }^(2) }} \\ \\ { \tt{ {x}^(2) + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^(2) = 7}} \\ { \tt{x + 3 = √(7) }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm √(7) )}}`