First, add color(red)(5) to each side of the equation to isolate the radical while keeping the equation balanced:
sqrt(x^2 + 2) - 5 + color(red)(5) = 0 + color(red)(5)
sqrt(x^2 + 2) - 0 = 5
sqrt(x^2 + 2) = 5
Next, square each side of the equation to eliminate the radical while keeping the equation balanced:
(sqrt(x^2 + 2))^2 = 5^2
x^2 + 2 = 25
Then, subtract color(red)(2) from each side of the equation to isolate x^2 while keeping the equation balanced:
x^2 + 2 - color(red)(2) = 25 - color(red)(2)
x^2 + 0 = 23
x^2 = 23
Now, take the square root of each side of the equation to solve for x while keeping the equation balanced. Remember, the square root of a number produces both a positive and a negative result:
sqrt(x^2) = +-sqrt(23)
x = +-sqrt(23)