completing the square solving for x

Question

2x^2-ax=6a^2

Answer 1

2x²-ax=6a²,

x²-ax/2=3a²,

x²-ax/2+a²/16-a²/16=3a² (completing the square: halve the x term and square the coefficient: ax/2→ax/4, coefficient (a/4)²),

(x-a/4)²=3a²+a²/16=49a²/16=(7a/4)²,

(x-a/4)²-(7a/4)²=0 (difference of two squares),

(x-a/4+7a/4)(x-a/4-7a/4)=0, so:

x-a/4+7a/4=0, and x=-3a/2 or:

x-a/4-7a/4=0, and x=2a.

Compare with factorising:

2x²-ax=6a²,

2x²-ax-6a²=(2x+3a)(x-2a), x=-3a/2 or 2a.