How do you complete the square and solve ##x^2+3x-28=0##?

##x =-7## and ##x = 4##

First, to factor the quadratic equation we need to play with integers which multiple to 28: 1,28 and 2,14 and 4,7

Trying combinations of these allows us to rewrite this problem as:

##(x + 7)(x - 4) = 0##

We can now solve for ##x + 7 = 0## and ##x - 4 = 0##

##x + 7 = 0 -> x + 7 - 7 = 0 - 7 -> x =-7##

##x - 4 = 0 -> x -4 + 4 = 0 + 4 -> x = 4##