Answer
$x=\{1.1789,5.1043\}$
Work Step by Step
$cos^2(x)-3cos(x)+1=0$
$cos(x)=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-3) \pm \sqrt{(-3)^2 - 4 (1)(1)}}{2(1)}=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$
$cos(x)=\frac{3-\sqrt{5}}{2}=0.3819$
$x=cos^{-1}(\frac{3-\sqrt{5}}{2})$
We know $cos(x)$ is positive in quadrant $I$ and $IV$
$x=1.1789\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;x=5.1043$
$cos(x)=\frac{3+\sqrt{13}}{2}\;\;\;\;$
$x=\{1.1789,5.1043\}$
