First, to solve the equation, you subtract 3 from both sides, then square both sides, subtract one from both sides, and finally divide by 2 on both sides. This indeed gets us x=4, but we also need to check if it's an extraneous solution. To do that we simply plug in x=4 into the original equation. sqrt( 2(4) + 1 ) + 3 = 0. When we do this, we end up with ±3 + 3 = 0. I do not agree, because we don't know if the sqrt(9) is -3 or 3.
