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:

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

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

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