Gress

Solve the equation by completing the square.

x^2+6x + 11 = 0

x = - 3±i sqrt (2)

Step-by-step explanation:

x^2+6x + 11 = 0

Subtract 11 from each side

x^2+6x + 11-11 = 0-11

x^2+6x = -11

Take the coefficient of the x terms

6

Divide by 2

6/2 = 3

Square it

3^2 = 9

Add it to each side

x^2+6x + 9 = -11+9

x^2 + 6x+9 = - 2

The left hand side becomes (x + (6/2)) ^2

(x+3) ^2 = - 2

Take the square root of each side

sqrt ((x+3) ^2) = ±sqrt (-2)

x+3 = ±sqrt (-2)

x+3 = ±i sqrt (2)

Subtract 3 from each side

x+3-3 = - 3±i sqrt (2)

x = - 3±i sqrt (2)