Answer
$p=9.37,-1.87$
Work Step by Step
$4p^2-40p+56=0$
or, $2p^2-15p+8=43$
or, $p^2-\frac{15}{2}p+4=\frac{43}{2}$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-10$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-\frac{15}{2})^2}{4}=\dfrac{225}{16}$
To complete the square, add $\dfrac{49}{4}$ on both sides.
$p^2-\frac{15}{2}p+4+\dfrac{225}{16}=\frac{43}{2}+\dfrac{225}{16}$
$\implies (p-\dfrac{15}{4})^2=\dfrac{505}{16}$
$\implies (p-\dfrac{15}{4})^2=31.57$
$\implies (p-3.75)^2=31.57$
$\implies (p-3.75)=5.62$
and
$\implies (p-3.75)=-5.62$
or, $p=9.37,-1.87$
