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,

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, May 17 '15 at 06:42
There are two solutions posted, one uses "completing the square" and the other uses the "quadratic formula". Take your pick. — Gregory Grant, May 17 '15 at 06:46

Gregory Grant · Answer 1 · 2015-05-17T07:44:08.013

4

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

edited May 17 '15 at 07:44

answered May 17 '15 at 06:41

Gregory Grant

14,874

To be symmetric: I'll upvote this answer. :-) – Kola B. May 17 '15 at 06:58
@KolaB. Thank you, wasn't fishing for it, but appreciated. :-) – Gregory Grant May 17 '15 at 06:58

score 3 · Answer 2 · answered May 17 '15 at 06:43

3

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

answered May 17 '15 at 06:43

Kola B.

2,465

Complete the square, yes. I'll upvote this answer – Gregory Grant May 17 '15 at 06:44

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

2 Answers2