How do you solve #4 x(x - 18) = - 288#?

1 Answer
George C.
Sep 26, 2016

#x = 12# or #x = 6#

Explanation:

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We use this later with #a=x-9# and #b=3#...

First note that both sides are divisible by #4#, so let's divide both sides by #4# to get:

#x(x-18) = -72#

Multiply out the left hand side and add #72# to both sides to get:

#0 = x^2-18x+72#

#color(white)(0) = x^2-18x+81-9#

#color(white)(0) = (x-9)^2-3^2#

#color(white)(0) = ((x-9)-3)((x-9)+3)#

#color(white)(0) = (x-12)(x-6)#

Hence:

#x = 12# or #x = 6#

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