# How do you factor #w^2 + 14w-1632=0#?

##### 1 Answer

Jul 19, 2016

#### Explanation:

**Method 1 - Completing the square**

#0 = w^2+14w-1632#

#= (w+7)^2-49-1632#

#= (w+7)^2-1681#

#= (w+7)^2-41^2#

#= ((w+7)-41))((w+7)+41)#

#= (w-34)(w+48)#

**Method 2 - Find pair of factors**

We want to find a pair of factors of

Since

Note that

So:

#sqrt(1632) ~~ 41.5#

#sqrt(1632)-7 ~~ 34.5#

#sqrt(1632)+7 ~~ 48.5#

Of the nearby numbers, find that

#w^2+14w-1632 = (w+48)(w-34)#