Solve the quadratic equation x2 − 5x + 6 = 0 by completing the square.

The given equation is $x^2 - 5x + 6 = 0$.
Subtract 6 from both sides:

To complete the square for an expression of the form $x^2 + bx$, we add $(\frac{b}{2})^2$.
In this equation, $b = -5$.
So, we need to add $(\frac{-5}{2})^2 = (\frac{25}{4})$ to both sides.

The left side factors as $(x - \frac{5}{2})^2$.
For the right side, find a common denominator: $-6 = -\frac{24}{4}$.

Add $\frac{5}{2}$ to both sides:

This gives two possible solutions:

And

The solutions are $x=2, x=3$.