Solve the equation x^2 + 4x + 4 = 0.
This is an example of Perfect Square Trinomial.
To check if it is a PST:
[tex] {x}^{2} \: + \: 4x \: + \: 4 \\2[( \sqrt{ {x}^{2})} \: ( \sqrt{4})] \\ 2[(x) \: (2)] \\ 2[(2x)] \\ = \: 4x[/tex]
Solving:
Find a number that when multiplied the answer is four and when added the answer is four as well.
[tex](x \: + \: 2)(x \: + \: 2)[/tex]
[tex] {x}^{2} \: + \: 2x \: + \: 2x \: + \: 4 \\ { \boxed{{x}^{2} \: + \: 4x \: + \: 4}}[/tex]