Answer :
The given equation is
[tex]p^2+4p=1[/tex]To use the completing square, divide 4p by 2 to find the product of the 2 terms of the bracket
[tex]\frac{4p}{2}=2p[/tex]Since 2p = 2 x p, then the bracket is (p + 2)
Let us make it power 2 and state its terms
[tex]\begin{gathered} (p+2)^2=(p)(p)+(p)(2)+(2)(p)+(2)(2) \\ (p+2)^2=p^2+2p+2p+4 \\ (p+2)^2=p^2+4p+4 \end{gathered}[/tex]We have already p^2 and 4p, then we must add 4, then
Add 4 to both sides of the equation
[tex]\begin{gathered} p^2+4p+4=1+4 \\ (p+2)^2=5 \end{gathered}[/tex]Now, let us take the square root to both sides
[tex]\begin{gathered} \sqrt[]{(p+2)^2}=\pm\sqrt[]{5} \\ p+2=\pm\sqrt[]{5} \end{gathered}[/tex]Subtract 2 from both sides
[tex]\begin{gathered} p+2-2=\pm\sqrt[]{5}-2 \\ p=\pm\sqrt[]{5}-2 \end{gathered}[/tex]The solutions of the equation are
[tex]p=\sqrt[]{5}-2,p=-\sqrt[]{5}-2[/tex]