OPSIE 1

\( \( \begin{align} {\left( {2p + 1} \right)^2} &= 16\\ 4{p^2} + 4p + 1 &= 16\\ 4{p^2} + 4p - 15 &= 0\\ 4\left[ {{p^2} + p - \frac{{15}}{4}} \right] &= 0\\ 4\left[ {{p^2} + p + {{\left( {\frac{1}{2}} \right)}^2} - {{\left( {\frac{1}{2}} \right)}^2} - \frac{{15}}{4}} \right] &= 0\\ 4\left[ {{{\left( {p + \frac{1}{2}} \right)}^2} - \frac{{16}}{4}} \right] &= 0\\ 4{\left( {p + \frac{1}{2}} \right)^2} - 16 &= 0\\ 4{\left( {p + \frac{1}{2}} \right)^2} &= 16\\ {\left( {p + \frac{1}{2}} \right)^2} &= 4\\ p + \frac{1}{2} &= \pm 2\\ p + \frac{1}{2} &= - 2\,\,&of&\,\,&p + \frac{1}{2} &= 2\\ p &= - \frac{5}{2} && &p &= \frac{3}{2} \end{align} \) \)

OPSIE 2

\( \begin{align} {\left( {2p + 1} \right)^2} &= 16\\ 4{p^2} + 4p + 1 &= 16\\ 4{p^2} + 4p &= 15\\ {p^2} + p &= \frac{{15}}{4}\\ {p^2} + p + {\left( {\frac{1}{2}} \right)^2} &= \frac{{15}}{4} + {\left( {\frac{1}{2}} \right)^2}\\ {\left( {p + \frac{1}{2}} \right)^2} &= 4\\ {\left( {p + \frac{1}{2}} \right)^2} &= 4\\ p + \frac{1}{2} &= \pm 2\\ p + \frac{1}{2} &= - 2 &of& &p + \frac{1}{2} &= 2\\ p &= - \frac{5}{2} && &p &= \frac{3}{2} \end{align} \)