Answer
$p=1.14,-6.14$
Work Step by Step
$p^2+5p-7=0$
or, $p^2+5p=7$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=5$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(5)^2}{4}=\dfrac{25}{4}$
To complete the square, add $\dfrac{25}{4}$ on both sides.
$p^2+5p+\dfrac{25}{4}=7+\dfrac{25}{4}$
$\implies (p+\dfrac{5}{2})^2=\dfrac{53}{4}$
$\implies (p+\dfrac{5}{2})=3.64$
and
$\implies (p+\dfrac{5}{2})=-3.64$
or, $p=1.14,-6.14$
