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Answer 1 · 2018-01-25T04:52:30

#x=+-4/3#

#9x^2-16=0#

Using the difference of squares, #a^2-b^2=(a-b)(a+b)#

#:.(3x-4)(3x+4)=0#

We get two solutions:

#3x-4=0#, #3x=4#, #x=4/3#

#3x+4=0#, #3x=-4#, #x=-4/3#

Combining the two solutions, we can write

#x=+-4/3#

Answer 2 · 2018-01-25T05:02:13

#9x^2-16=0#

Let's start by adding #color(red)(16)# to both sides

#9x^2 cancel(-16)cancelcolor(red)(+16) = 0 + color(red)(16)#

#9x^2 = 16#

Since we are solving for #x#, divide both sides by #9#

#(cancel9x^2)/cancel9 = 16/9#

#x^2=16/9#

Now take square root

#x=+-sqrt(16/9)#

Simplify it

#x= +-4/3#