Question

Solve: $p^2-12p+32=0$.

Answer 1

Given quadratic equation is $p^2-12p+32=0$

By splitting the middle term, we can factorize the given quadratic equation.

Here we need to select two terms such that their sum is '$-12p$' and their product is '$32p^2$'.

Clearly $-8p-4p=-12p$ and $(-8p)\times (-4p)=32p^2$

So, $p^2-12p+32=0$

$\Rightarrow p^2-8p-4p+32+0$

$\Rightarrow p(p-8)-4(p-8)=0$

$\Rightarrow (p-8)(p-4)=0$

$\Rightarrow p-8=0$ and $p-4=0$

$\Rightarrow p=8$ and $p=4$.