Answer:
Step-by-step explanation:
rewrite 9-6x+[tex]x^{2}[/tex] as [tex]x^{2}[/tex]-6x+9. (this step isn't necessary, but it's easier when the bigger term is in front)
There's two ways: using the quadratic formula, or just doing it in your head (for simple ones)
For the simple way:
think about what numbers not only multiply to equal c (represented by 9 in this case) but also add to equal -6 (represents b in this problem). There are two numbers for this problem that work: -3 and -3. So you would write the factored form as (x-3)(x-3)
Quadratic formula:
The formula is [tex]\frac{-b}{2a}[/tex] ±[tex]\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
This formula works for equations in the form of a[tex]x^{2}[/tex]+bx+c.
Substitute in the values to get:
[tex]\frac{6}{2} +\frac{\sqrt{-6^{2} -4(1)(9)} }{2}[/tex]
simplify:
3±[tex]\frac{\sqrt{36-36} }{2}[/tex]
3±[tex]\frac{0}{2}[/tex]
the answer is 3, which is the x-intercept. Write that as (x-3)(x-3)
