Question

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

Answer 1

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

Answer 2

Is this correct?

Answer 3

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

Answer 4

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

Answer 5

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?

Answer 6

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

Answer 7

Pretty close. \(\pi + other\;stuff\).

Answer 8

Okay, thanks!

Answer 9

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.