How do I solve a quadratic equation by completing the square if the a variable has a number attached to it (3a² + b = 2)

Question

So in the equation 3a² + b = 2, how do I solve it by completing the square when I have 3 attached to a²

Answer 1

Divide the equation by the number in front of a², then work as normal.

 

However, there's a shortcut.

 

First arrange the equation into its general form, ax² + bx + c = 0.

 

Second, find the values of the following two equations: d = b/2a and e = c - b²/2a

 

Third, plug the values into: a(x+d)² + e = 0