Need help finding the intersecting points between curves?

Question

So, basically, I'm trying to find the intersection points between curves. I get the gist of how to do it: You set them equal, get one side to zero, then factor, you have your two roots. But when I do it, all of my answers are unfactorable.

Example, for y = x^2-2x+8 and y = x+6
I set them equal
 x^2-2x+8 = x+6
then set one side to 0
x^2-3x+14 = 0
And then... oh, this is unfactorable. 
But then if I put them into a graph, I can see they intersect at 1 and 2. What am I doing wrong? That was the first question from my homework, so I think it should be doable. 
Thanks in advance

Brenda · Accepted Answer

x²-2x+8=x+6

x²-3x+2=0

(x-1)(x-2)=0

x=1 and x=2

RATTY · Answer

The curve y = x^2 - 2x + 8 intersects with the line y = x+6 when:

x^2 - 2x + 8 = x + 6 

=>  x^2 - 3x + 2 = 0  This is where you have gone wrong.  We are subtracting 6 from both sides.

Now solve this quadratic for x by factorising:

=>  x^2 -2x - x + 2  = 0

=>  x(x - 2) - 1(x - 2) = 0

=>  (x - 2)(x -1) = 0

=>  x = 2 or x = 1

When x = 2, y = 2 + 6 = 8

When x = 1, y = 1 + 6 = 7

Answer:  the intersecting points of the curves are (2,8) and (1,7)

Raffaele · Answer

I set them equal
x^2-2x+8 = x+6   <---   x^2 - 2 x + 8 - x - 6 = 0
then set one side to 0
x^2-3x+14 = 0   <--- it's wrong: should be x^2 - 3x + 2 = 0

? · Answer

x^2-2x+8 = x+6
x^2-3x+2 = 0
(x-2)(x-1) = 0
x = 1 and 2

Need help finding the intersecting points between curves?

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