To find $x$ in $x^2 -8x-11=0$

Question

$x^2 -8x-11=0$

I have tried factorising but it won't factorise into a quadratic equation

Hi, It would be great if you could complete this question with working and post it. Thx

The two solutions of $x^2 -8x -11=0$ are in the form $x=p +\- Q root 3$ where p and q are both intergers. Find p and q. – Jason 2 mins ago edit delete

That's the full question,

Answer 1

$a=1$, $b=-8$, $c=-11$. The quadratic formula says the roots are $$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ $$=\frac{8\pm\sqrt{64+44}}{2}$$ $$=4\pm\frac12\sqrt{108}$$ $$=4\pm\frac12\sqrt{36\cdot3}$$ $$=4\pm3\sqrt{3}$$

Answer 2

HINT: (Without any knowledge about quadratic formula): $$ x^2−8x−11=(x-4)^2-11-16=(x-4)^2-\sqrt{27}^2. $$