Verify my answer for: Find all solutions to the equation.
cos^2x+2cosx+1=0

Question

Verify my answer for: Find all solutions to the equation.
cos^2x+2cosx+1=0

anonymous · Answer

Factor the equation.
cos^2x+cosx+cosx+1=0
cosx(cosx+1)+(cosx+1)=0
(cosx+1)^2=0
Solve the quadratic.
cosx+1=0
cosx=-1
x=pi

anonymous · Answer

Is this correct?

tkhunny · Answer

Are we restricted to $x\in[0,2\pi)$

anonymous · Answer

Sorry, I was away from my computer for a moment. It didn't say. @tkhunny

tkhunny · Answer

Oh, then you will have to be more general.  $x = \pi$ is only one of infinitely many solutions.  Can you name them all with one expression?

anonymous · Answer

"pi*(n*2pi), n= 1, 2, 3, ..."? @tkhunny

tkhunny · Answer

Pretty close.  $\pi + other\;stuff$.

anonymous · Answer

Okay, thanks!

tkhunny · Answer

Usually, $\pi + 2k\pi$ for k and integer.  This gets all the positive and negative multiples of $2\pi$ from $\pi$.  You've only the positive multiples.