Solve x^2 + 4x + 4 = 0

To solve this equation we have two different methods:

1) We can solve this method 'by hand' and is done by knowing how to factorise the quadratic and is done by looking at the equation given to us to find hints that will help solve it.

(x " first symbol " a) (x " second symbol" b) = 0

WIthout going too in depth:

the second symbol "+" tells us that the two symbols in our answer are the same

the first symbol "+" combined with the knowledge of second symbol "+" tells us that the two symbols in our answer are both "+"

next we know "a" times "b" = 4 and "a" + "b" = 4 so we find numbers that match this description e.g. 2 and 2 and so we have found our answer

x^2 + 4x + 4 = 0 = (x+2)(x+2) 

and so x = -2 

2) Using the quadratic formula:

 (-b +- sqrt(b^2 - 4ac))/2

This method is simpler and requires you to only plug in the numbers in the correct place of the formula, the a, b and c from the formula come from the general equation: ax^2 + bx + c which all quadratic formulas can be related to. 

e.g.) ax^2 + bx + c and so a = 1, b = 4 c = 4 in our example

and our result is -2