# Factoring question

1. Jan 31, 2010

### zeion

1. The problem statement, all variables and given/known data

I need to find the point at which these functions intersect:
y = -sqrt(x)
y = x - 6

2. Relevant equations

3. The attempt at a solution

I set them to equate:
-sqrt(x) = x - 6
-sqrt(x) - x + 6 = 0

Now how do I find the root?

2. Jan 31, 2010

### icystrike

equate them tgt , $$\sqrt{x}=6-x$$ .
Now square both sides , x=36+x²-12x ... continue from here.

3. Jan 31, 2010

### zeion

Do I move them all to one side and get x^2 -13x + 36 = 0?

4. Feb 1, 2010

### Staff: Mentor

Yes. Now factor.

Be sure to check each solution in the original equation, though. When you square both sides of an equation, extraneous solutions are sometimes introduced, values that are not solutions of your original equation.

5. Feb 1, 2010

### ideasrule

Alternatively, you can say u=sqrt(x) and rewrite the equation as -u-u^2+6=0

6. Feb 1, 2010

### zeion

Okay nice.
So I can't use x = 9 because -sqrt(9) not= 9-6, correct?

7. Feb 1, 2010

### zeion

Ah okay, that u substitution seems easier:
Let u = sqrt(x), then
u^2 + u - 6 = 0
(u+3)(u-2) = 0
u = -3, u = 2
sqrt(x) = -3, sqrt(x) = 2
x = 9, x = 4

8. Feb 1, 2010

Thanks guys!

9. Feb 1, 2010

### Staff: Mentor

But x = 9 is not a solution of sqrt(x)= 6 -x, which is what you started with. x = 9 is an extraneous solution that I warned you of.