How do you factor #-4/3x+4/9=-x^2#?

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Answer 1 · 2017-08-15T23:45:19

#x^2-4/3x+4/9=color(blue)((x-2/3)^2#

Refer to the explanation for the process.

Factor:

#-4/3x+4/9=-x^2#

Add #x^2# to both sides.

#x^2-4/3x+4/9=0#

Since the desired answer is the factors of the equation, the #0# will not be included in the expression.

Find two numbers that when added equal #-4/3# and when multiplied equal #4/9#. Both requirements are met by #-2/3#.

#x^2-4/3x+4/9=(x-2/3)(x-2/3)#

#x^2-4/3x+4/9=(x-2/3)^2#