Question

Find all solutions for 2cos^2x+3cosx+1=0

Answer 1

it's very hard to see ir because of the "Cosx" sign there.
Sinve we want to make things more evident and simple to solve we will make a "change of variable".
So, let's take a look at the problem:
\[2Cos ^{2}x+3Cosx+1=0\]
And let's make the change of variable:
\[z=Cosx\]
And replace it:
\[2z ^{2}+3z+1=0\]
And now, we formed a quadratic equation wich we can solve with the general formula:
\[z=\frac{ -3 \pm \sqrt{3^{2}-4(2)(1)} }{ 2(3) }\]
I believe you can go on from here, once you found the values of "z", go to the change of variable and deduce the value of x.