Answer:
x = a/2 + 6.5 a^2
Step-by-step explanation:
x^2-ax-6a^2=0
Assuming a is a constant, let's move the third term to the right:
x^2-ax=6a^2
Now we need to add something to both sides to make it a perfect square.
x^2-ax + _____ = 6a^2 + ______
We need to add a/2 ^2 to both sides. (This is a standard part of completing the square, wherein you add b/2 ^2. Like if you had 8x as your middle term, you add 16.)
x^2-ax + a/2 ^2 = 6a^2 + a/2 ^2
Factor the left side, because it's a perfect square now:
(x - a/2)(x - a/2) = 6.5 a^2
(x - a/2)^2 = 6.5 a^2
Take the square root of both sides:
x - a/2 = 6.5 a^2
x = a/2 + 6.5 a^2
