How do you factor #3x ^ { 2} + 15x + 21= 0#?

1 Answer
Taha Z.
Sep 14, 2017

#3(x^2+5x+7)=0#

Explanation:

#3x^2+15x+21=0#+

Since all terms are divisible by 3, we take 3 as a common factor:
#3(x^2+5x+7)=0#

We can further go and simplify the equation:

We divide the whole equation by 3:
#(3x^2+15x+21=0)/3#
#rarrx^2+5x+7=0#

Then we use the reverse of #(a+b)^2=a^2+2ab+b^2#, in our case #a=x#
#2ab=5x#
#rarr 2(x)b=5x#

Dividing the equation by #x# and then by 2:
#(2cancelxb)/cancelx=(5cancelx)/cancelx#
#(cancel2b)/cancel2=5/2#
#b=2.5#

Now we can write the equation in form #a^2+2ab+b^2#:
#x^2+5x+(2.5)^2-(2.5)^2+7=0#
#(x+2.5)^2-6.25+7=(x+2.5)^2+0.25#
#(x+2.5)^2cancel(+0.25)cancel(-0.25)=0-0.25#
#(x+2.5)^2=-0.25#

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