Answer
The solutions are $x=2+\sqrt{3}\approx 3.73$ and $x=2-\sqrt{3}\approx 0.27$.
Work Step by Step
The given equation is
$\Rightarrow x^2-4x+1=0$
Subtract $1$ from each side.
$\Rightarrow x^2-4x+1-1=0-1$
Simplify.
$\Rightarrow x^2-4x=-1$
The coefficient of the $x^2-$term is $1$, and the coefficient of the $x-$term is an even number.
So, solve by completing the square.
$\Rightarrow x^2-4x=-1$
Add $(\frac{b}{2})^2=(\frac{-4}{2})^2=4$ to each side.
$\Rightarrow x^2-4x+4=-1+4$
Write the left side as the square of a binomial.
$\Rightarrow (x-2)^2=3$
Take the square root of each side.
$\Rightarrow x-2=\pm\sqrt{3}$
Add $2$ to each side.
$\Rightarrow x-2+2=2\pm\sqrt{3}$
Simplify.
$\Rightarrow x=2\pm\sqrt{3}$
The solutions are $x=2+\sqrt{3}\approx 3.73$ and $x=2-\sqrt{3}\approx 0.27$.
