complete the square. 6x^2+6x+3=0

Question

Solve the problem by completing the square.

Answer 1

6x² + 6x + 3 = 0

Separate variables and constants aside by subtracting 3 from each side 

6x² + 6x = -3

Here x² coefficient is 6, for perfect square make x² coefficient 1 by dividing each side by 6

x²  + x = - ½

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

Here x coefficient = 1. So, (half the x coefficient)² = (1/2)²= 1/4
Add 1/4 to each side 
x²  + x + 1/4= - 1/2 + 1/4

(x + 1/2) ²= -1/4

 

Take square root both sides 

x + 1/2 = ±√(1/4i²⁾

x + 1/2 = ±(1/2) i

 

subtract 1/2 from each side

x = -1/2 ±(1/2)i

 

Roots are

x = -1/2 + (1/2)i

x = -1/2 - (1/2)i