How do you complete the square and solve ##x^2+3x-28=0##?
February 20th, 2023
##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##