How do you solve $x^2-x-1=0$ by completing the square?

Question

36123 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-24T11:45:42

We have

$x^2-x-1=0$

$x^2-2*1/2*x+(1/2)^2-5/4=0$

$(x-1/2)^2-5/4=0$

$(x-1/2)^2=5/4$

Taking square roots in both sides

$|x-1/2|=sqrt5/2$

and

$(x-1/2)=+- sqrt5/2$

Hence the two solutions are

$x_1=1/2+sqrt5/2$ and $x_2=1/2-sqrt5/2$

How do you solve x^2-x-1=0x^2-x-1=0 by completing the square?