Answer:
C
Step-by-step explanation:
We have the equation:
[tex]x^2-6x=10[/tex]
We can subtract 10 from both sides:
[tex]x^2-6x-10=0[/tex]
Since this equation isn't factorable, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -6, and c = -10.
Substitute:
[tex]\displaystyle x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-10)}}{2(1)}[/tex]
Simplify:
[tex]\displaystyle x=\frac{6\pm\sqrt{76}}{2}[/tex]
Note that:
[tex]\sqrt{76}=\sqrt{4\cdot 19}=2\sqrt{19}[/tex]
Hence:
[tex]\displaystyle x=\frac{6\pm2\sqrt{19}}{2}=3\pm\sqrt{19}[/tex]
Therefore, our answer is C.
