If x^2 = 16, why isn't the answer just x = 4?

You're right that x = 4 is a solution to the equation - but the problem is it's not the only solution, x = -4 also works.You have to be careful not to take a shortcut by simply taking the square root of both sides of the equation, because the square root of 16 is plus or minus 4. Forgetting to include "plus or minus" every time you square root an equation is a very easy mistake to make, but luckily there's another method for solving this equation...Move all the terms in the equation to one side of the equals sign;x^2 - 16 = 0Because the left hand side is a "difference of two squares" it can easily be factorised;(x - 4)(x + 4) = 0So, x - 4 = 0 or x + 4 = 0.Therefore x = 4 or x = -4.This is the normal way we solve quadratic equations, and it means we are much less likely to make a silly mistake!