Question 173413
p2 + 3p - 9 = 0. 

Add 9 to both sides of the equation

p2 + 3p=9


Divide the coefficient of the p term(=3) term by 2 and square the resultant  value and add to both sides of the equation

p2 +3p +(3/2)^2= 9 +(3/2)^2

This makes the quadratic equation a perfect square

(p+3/2)^2=9 +9/4

Simplify the left side of the equation

(p+3/2)^2=36/4+9/4=45/4
(p+3/2)^2=45/4

Take the square root of both sides 

p+3/2= + or -3sqrt5/2
subtract 3/2 from  both sides

p=-3/2+3sqrt5/2 or p=-3/2-3sqrt5/2