First, get your quadratic equation to the form
#color(blue)(x^2 + b/ax = -c/a)#
To do that, add #5# to both sides of the equation
#x^2 + 2x - color(red)(cancel(color(black)(5))) + color(red)(cancel(color(black)(5))) = 5#
#x^2 + 2x = 5#
Next, divide the coefficient of the #x#-term by 2, square the result. then add it to both sides of the equation.
#2/2 = 1#, then #1^2 = 1#
This will get you
#x^2 + 2x + 1 = 5 + 1#
Notice that you can rewrite the left side of the equation as the square of a binomial
#x^2 + 2x + 1 = x^2 + 2 * (1) * x + 1^2 = (x+1)^2#
You will now have
#(x + 1)^2 = 6#
Take the square root of both sides
#sqrt((x+1)^2) = sqrt(6)#
#x + 1 = +- sqrt(6) => x_(1,2) = -1 +- sqrt(6) = {(x_1 = color(green)(-1 - sqrt(6))), (x_2 = color(green)(-1 + sqrt(6))) :}#
