Question

Gress
Solve the equation by completing the square.
x^2+6x + 11 =0

Answer 1

x = -3±i sqrt(2)

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)