piarepm

2021-12-10

Solve using the method of factorization:

$32-{x}^{2}=4x$

nghodlokl

Beginner2021-12-11Added 33 answers

Consider $32-{x}^{2}=4x$

$\Rightarrow {x}^{2}+4x-32=0$

We now find 2 numbers, say p and q such that

pq=-32 and p+q=4

And the equation becomes:

${x}^{2}+px+qx-32=0$

We take p=8, q=-4

Thus

$\Rightarrow {x}^{2}+8x-4x-32=0$

$\Rightarrow x(x+8)-4(x+8)=0$

$\Rightarrow (x-4)(x+8)=0$

By method of factorization we have

Either (x-4)=0 or (x+8)=0

$\Rightarrow x=4,x=-8$

Hence the solutions are

x=4, -8

We now find 2 numbers, say p and q such that

pq=-32 and p+q=4

And the equation becomes:

We take p=8, q=-4

Thus

By method of factorization we have

Either (x-4)=0 or (x+8)=0

Hence the solutions are

x=4, -8