# How do you solve x^2 - 5x+ 6 = 0?

Jan 11, 2018

$\textcolor{b l u e}{x = 2 \mathmr{and} x = 3}$

#### Explanation:

Given:

${x}^{2} - 5 x + 6 = 0$

Step.1

Consider

$y = f \left(x\right) = {x}^{2} - 5 x + 6 = 0$

Split the middle term of the Quadratic Expression:

${x}^{2} - 3 x - 2 x + 6 = 0$

We can rewrite this in factor form:

$x \left(x - 3\right) - 2 \left(x - 3\right) = 0$

Hence,

the factors are: $\left(x - 3\right) \mathmr{and} \left(x - 2\right)$

This would mean

either $\left(x - 3\right) = 0 \mathmr{and} \left(x - 2\right) = 0$

Now we can write our solutions as

$\textcolor{b l u e}{x = 2 \mathmr{and} x = 3}$

We can also graph our quadratic to verify our solutions

We analyze the graph and note the following:

x-intercepts are: $\left(2 , 0\right) , \left(3 , 0\right)$

Hence, our solutions are verified.

Some additional pieces of useful information for you:

Vertex is at $\left(2.5 , - 0.25\right)$

And,

Axis of Symmetry is at $x = 2.5$