2x^2+20x=-38 divide both sides by 2
x^2+10x=-19, halve the linear coefficient, square it, than add that value to both sides of the equation, in this case add (10/2)^2=25...
x^2+10x+25=6 now the left side is a perfect square
(x+5)^2=6 take the square root of both sides
x+5=±√6 subtract 5 from both sides
x=-5±√6 (so answer c.)
