How do you solve #-16p^2-64p-64=0# by factoring?

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Answer 1 · 2015-08-20T13:36:59

The solution is
#color(green)(p=-2#

#-16p^2-64p-64=0#

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like #ap^2 + bp + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = -16*-64 = 1024#
and
#N_1 +N_2 = b = -64#

After trying out a few numbers we get #N_1 = -32# and #N_2 =-32#

#-32*-32 = 1024#, and

#(-32)+(-32)= -64#

#-16p^2-64p-64=-16p^2-32p-32p-64#

# = -16p(p+2) - 32(p+2)=0#

#(p+2)# is a common factor to each of the terms

#color(green)((-16p-32)(p+2)=0#

we now equate the factors to zero:

#-16p-32=0, -16p=32, color(green)(p=-2#

#p+2=0, color(green)(p=-2#