Solve the equation x² − 5x + 6 = 0

Answer: \(x=2\) or \(x=3\).

Key steps

Factor the expression:

\[ x^2-5x+6=(x-2)(x-3) \]

This works because \((-2)+(-3)=-5\) and \((-2)(-3)=6\).

Now solve:

\[ (x-2)(x-3)=0 \]

A product equals \(0\) when at least one factor equals \(0\):

\[ x-2=0 \Rightarrow x=2 \]

or

\[ x-3=0 \Rightarrow x=3 \]

Check

For \(x=2\):

\[ 2^2-5\cdot2+6=4-10+6=0 \]

For \(x=3\):

\[ 3^2-5\cdot3+6=9-15+6=0 \]

Both solutions are correct.