How do you solve #x^2+18x=-17# by factoring?

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Answer 1 · 2016-12-20T13:41:35

#x = -1# and #x = -17#

First, we need to get this problem in standard quadratic equation form by equating it to #0#:

#x^2 + 18x + color(red)(17) = -17 + color(red)(17)#

#x^2 + 18x + 17 = 0#

Now we factor:

#(x + 1)(x + 17)= 0#

To solve we equate each term to #0# and solve for #x#:

Solution 1):

#x + 1 = 0#

#x + 1 - color(red)(1) = 0 - color(red)(1)#

#x + 0 = -1#

#x = -1#

Solution 2):

#x + 17 = 0#

#x + 17 - color(red)(17) = 0 - color(red)(17)#

#x + 0 = -17#

#x = -17#