Question

What re the solutions of the equation x^2 +4x+4 = 25?

Answer 1

Get everything on one side: $x^{2} +4x-21=0$.  Now we can factor to find the solutions.  What we ask ourselves here is "What 2 numbers will add to be +4 and multiply to be -21?"  +7 and -3 work because 7-3 = 4 and 7 * -3 = -21.  So our factors are (x+7)(x-3).  Our solutions, however, are found using the Zero Product Property.  If x + 7 = 0, then x = -7.  If x - 3 = 0, then x = 3.  So our solutions are x = -7 and x = 3.