completing the square

Question

Solve the equation by completing the square. state whether the solutions are real or non-real.

3x^2+2x+1=0

I solved and got (−1+√2i)/3,(−1-√2i)/3
I am not sure if it is real or not

Answer 1

Your roots are correct. Outstanding job on completing the square!

Answer 2

Subtract 1 to both sides of the equation to isolate the x terms.

 

3x² + 2x = -1

 

 

Divide both sides of the equation by 3.

 

x² + (2/3)x = -1/3

 

 

Add 1/9 to both sides of the equation.

 

x² + (2/3)x + (1/9) = -1/3 + 1/9

 

(x + 1/3)² = (-3/9) + (1/9)

 

(x + 1/3)² = -2/9

 

 

Square-root both sides of the equation.

 

x + 1/3 = ±√(-2/9)

 

x + 1/3 = ±√(-2) / 3

 

x = (-1/3) ± √(-2)/3

 

x = (-1/3) ± i√(2)/3

 

x = (-1 ± i√(2)) / 3

 

 

You are correct!  And it is imaginary.