Step 1: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 2 , b = 17 ~ \text{ and } ~ c = -55 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -55} $.

$$ a \cdot c = -110 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -110 $ and add to $ b = 17 $.

Step 4: All pairs of numbers with a product of $ -110 $ are:

PRODUCT = -110
-1     110	1     -110
-2     55	2     -55
-5     22	5     -22
-10     11	10     -11

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 17 }$

PRODUCT = -110 and SUM = 17
-1     110	1     -110
-2     55	2     -55
-5     22	5     -22
-10     11	10     -11

Step 6: Replace middle term $ 17 x $ with $ 22x-5x $:

$$ 2x^{2}+17x-55 = 2x^{2}+22x-5x-55 $$

Step 7: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ -5 $ out of the last two terms.

$$ 2x^{2}+22x-5x-55 = 2x\left(x+11\right) -5\left(x+11\right) = \left(2x-5\right) \left(x+11\right) $$

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