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}
