Hi Can you help? Find the value of p if the quadratic expression x^2-(p+2)x + p + 5 = 0 is a perfect square. Thanks?

x² - (p + 2)x + (p + 5) = 0
x² - (p + 2)x = - (p + 5)
x² - 2[(p + 2)/2]x = - (p + 5)
x² - 2[(p + 2)/2]x + [(p + 2)/2]² = - (p + 5) + [(p + 2)/2]²
{x² - [(p + 2)/2]}² = - (p + 5) + [(p + 2)/2]²

Since it is a perfect square, then - (p + 5) + [(p + 2)/2]² = 0
4 {- (p + 5) + [(p + 2)/2]²} = 0
-4(p + 5) + (p + 2)² = 0
-4p - 20 + p² + 4p + 4 = 0
p² - 16 = 0
p² - 4² = 0
(p + 4)(p - 4) = 0
p = -4 or p = 4

ax^2+bx+c=0
a=1
b=-(p+2)
c= p+5

b^2-4ac = 0 (discriminant = 0)
(p+2)^2 = 4 (1)(p+5)
p^2+4p+4 = 4p+20
p^2 =16
p = -4 or 4