solve the equation for x by completing the square
x^2 = kx + 1

Question

solve the equation for x by completing the square
 x^2 = kx + 1

anonymous · Answer

Do you know how to complete the square?

anonymous · Answer

@wombat yeee

anonymous · Answer

So what is confusing?

anonymous · Answer

i did this 

x^2 = kx-1 =0
x^2 - kx = 1
x^2 - kx + k^2/x = 1

and I'm stuck there

anonymous · Answer

The problem is that you have added the term k^2/x spontaneously.  In mathematics, it is important that you perform the same operation to both sides.

anonymous · Answer

i meant k^2/4 not k^2/x
so it should be x^2 - kx + k^2/4 = 1 - k^2/4

anonymous · Answer

? *

anonymous · Answer

That looks to be correct.

directrix · Answer

x^2 - kx + k^2/4 = 1 - k^2/4

[x - (k/2)] ^2 = 4/4 - k^2/4

[x - (k/2)] ^2 = (4 - k^2)/4

What comes next?

anonymous · Answer

[x- (k/2)]^2 = (4/x - k^2/4)
x- k/2 = √ k^2/2 + 4
x = (k + √k^2 +4)/2, x=(k-√k^2+4)/2

directrix · Answer

That's what I got. You may need another grouping symbol.

x =[ (k + √(k^2 +4)] / 2

x =[ (k - √(k^2 +4)] / 2

That shows clearly what the radicand is.