piarepm

2021-12-10

Solve using the method of factorization:
$32-{x}^{2}=4x$

### Answer & Explanation

nghodlokl

Consider $32-{x}^{2}=4x$
$⇒{x}^{2}+4x-32=0$
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
$⇒{x}^{2}+8x-4x-32=0$
$⇒x\left(x+8\right)-4\left(x+8\right)=0$
$⇒\left(x-4\right)\left(x+8\right)=0$
By method of factorization we have
Either (x-4)=0 or (x+8)=0
$⇒x=4,x=-8$
Hence the solutions are
x=4, -8

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