### Let $x$ be a real number. What is the minimum value of $x^2 - 4x + 3$?

$-1$
1. We are given a quadratic equation $x^2 - 4x + 3$, where x is a real number and we need to find the minimum value of this equation.
\begin{align} x^2 - 4x + 3 & = x^2 - 4x + 4 - 1 \\ & = x^2 - 2(2)x + 2^2 - 1 \\ & = (x - 2)^2 - 1 \end{align}
3. Observe that the value of $x^2 - 4x + 3$ will be minimum when $(x - 2)^2 = 0, i.e. \space x = 2$
The value of $x^2 - 4x + 3$ at $x = 2$ is $-1$.
4. Hence, the minimum value of $x^2 - 4x + 3$ is $-1$.