Solve for x by completing the squares: ax^2-x+2=0
Please show all the steps.

Question

Solve for x by completing the squares: ax^2-x+2=0
Please show all the steps.

anonymous · Answer

really? this is icky

anonymous · Answer

$$ax^2-x=-2$$ 
$$x^2-\frac{1}{a}x=-\frac{2}{a}$$
$$(x-\frac{1}{2a})^2=-\frac{2}{a}+\frac{1}{4a^2}$$
$$(x-\frac{1}{2a})^2=\frac{1-8a}{4a^2}$$

anonymous · Answer

take the square root of both sides, get 
$$x-\frac{1}{2a}=\pm\frac{\sqrt{1-8a}}{2a}$$ then solve for $x$
$$x=\frac{1\pm\sqrt{1-8a}}{2a}$$

anonymous · Answer

@Mertsj  please don't tell me i screwed this up

anonymous · Answer

Thank you so much!

mertsj · Answer

yw

anonymous · Answer

no i think i added the fractions correctly

anonymous · Answer

$$\frac{1}{4a^2}-\frac{2}{a}=\frac{1-8a}{4a^2}$$

mertsj · Answer

yep.  Somewhere I dropped the denominator fron the 2.  Just getting tooooo old.

anonymous · Answer

wait until you get my age...

mertsj · Answer

I'm sure I'm older than you already.

anonymous · Answer

i would not bet on it

mertsj · Answer

Does that 73 mean something?

anonymous · Answer

but we will leave it a mystery

anonymous · Answer

well yes, but not my age !!

anonymous · Answer

it is satellite73 as in what i drive

mertsj · Answer

Very cool.

anonymous · Answer

thanks
i was trying to find a picture but they seem to be either hot rods or beaters, and mine is neither

mertsj · Answer

Did you restore it yourself?

anonymous · Answer

What if the equation is like this: x^2+ax-2=0?

mertsj · Answer

It is easier because the coefficient of the x^2 term is already 1.

mertsj · Answer

Just take 1/2 of a, square it and add it to both sides.  First, of course move the 2 to the right side.