Answer:
[tex]x=1\pm\sqrt{10}[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where [tex]0 = ax^2 + bx + c[/tex].
For the given quadratic:
[tex]0=x^2-2x-9[/tex]
we can identify the variable values:
- [tex]a=1[/tex]
- [tex]b=-2[/tex]
- [tex]c=-9[/tex]
Plugging these into the quadratic formula, we get:
[tex]x=\dfrac{-(-2)\pm\sqrt{2^2-4(1)(-9)}}{2(1)}[/tex]
[tex]x=\dfrac{2\pm\sqrt{4+36}}{2}[/tex]
[tex]x=\dfrac{2\pm\sqrt{40}}{2}[/tex]
[tex]x=\dfrac{2\pm\sqrt{4 \cdot 10}}{2}[/tex]
[tex]x=\dfrac{2\pm2\sqrt{10}}{2}[/tex]
[tex]\boxed{x=1\pm\sqrt{10}}[/tex]
