First, add #color(red)(50)# to each side of the equation to isolate the #n# term while keeping the equation balanced:
#2n^2 - 50 + color(red)(50) = 0 + color(red)(50)#
#2n^2 - 0 = 50#
#2n^2 = 50#
Next, divide each side of the equation by #color(red)(2)# to isolate #n^2# while keeping the equation balanced:
#(2n^2)/color(red)(2) = 50/color(red)(2)#
#(color(red)(cancel(color(black)(2)))n^2)/cancel(color(red)(2)) = 25#
#n^2 = 25#
Now, take the square root of each side of the equation to solve for #n# while keeping the equation balanced. Remember, the square root of a number produces a positive and negative result.
#sqrt(n^2) = +-sqrt(25)#
#n = +-5#
The Solution Set Is:
#n = {-5, 5}#
