Step 1: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = -20 } ~ \text{ and } ~ \color{red}{ c = 99 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -20 } $ and multiply to $ \color{red}{ 99 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 99 }$.

PRODUCT = 99
1     99	-1     -99
3     33	-3     -33
9     11	-9     -11

Step 3: Find out which pair sums up to $\color{blue}{ b = -20 }$

PRODUCT = 99 and SUM = -20
1     99	-1     -99
3     33	-3     -33
9     11	-9     -11

Step 4: Put -9 and -11 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-20x+99 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-20x+99 & = (x -9)(x -11) \end{aligned} $$

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