# Thread: How should I solve this?

1. ## How should I solve this?

Solve: $x^4-2x^3-2x-1=0$

I got the right solution, but I don't think I went about it the right way... I think I just had a lucky guess. How would you solve this?

2. ## hint

$x^4-2x^3-2x-1=x^4-2x^3-x^2+x^2-2x-1=(x^4-2x^3-x^2)+(x^2-2x-1)$
Can you proceed from here?

--Kevin C.

3. Originally Posted by TwistedOne151
$x^4-2x^3-2x-1=x^4-2x^3-x^2+x^2-2x-1=(x^4-2x^3-x^2)+(x^2-2x-1)$
Can you proceed from here?

--Kevin C.
How did you know which $x^2$ to pick?

4. Originally Posted by TwistedOne151
$x^4-2x^3-2x-1=x^4-2x^3-x^2+x^2-2x-1=(x^4-2x^3-x^2)+(x^2-2x-1)$
Can you proceed from here?

--Kevin C.
Kevin: Is there some "method" you used to factor this equation? If so, would you mind showing me ALL (and perhaps others) the steps involved? Or, do you have that rare abilitiy where you just can look at an equation like the one Christopher listed and somehow "see" its factors?

I would appreciated it because I worked on this equation for quite a while and I could not figure out how exactly to factor it.

5. ## reorder the terms

Originally Posted by ChristopherDunn
Solve: $x^4-2x^3-2x-1=0$
reorder the terms

$x^4-1-2x^3-2x=0$

then

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

$(x^2+1)(x^2-2x-1)=0$

$x=1-\sqrt{2}$
$x=1+\sqrt{2}$