# How do you solve x² - 5x + 6 = 0?

Jun 25, 2015

The solutions are
color(green)(x=2, x=3

#### Explanation:

${x}^{2} - 5 x + 6 = 0$
Here we can first factorise the expression and then find the solution:

Factorising by splitting middle term
${x}^{2} \textcolor{g r e e n}{- 2 x - 3 x} + 6 = 0$

$x \left(x - 2\right) - 3 \left(x - 2\right) = 0$
color(green)( (x-2)(x-3) =0
Equating the two factors with zero to obtain solutions:

• x-2 = 0 ,color(green)( x=2
• x-3 = 0 , color(green)(x=3