I solved √(x + 6) = x and got x = 3 and x = −2, but only x = 3 works when I check it.
Accepted answer
Because **squaring both sides isn't reversible** — it can create solutions the original equation never had.
Squaring destroys sign information: `3` and `−3` both square to `9`. So when you square `√(x + 6) = x`, you're really solving `x + 6 = x²`, which also captures the case `√(x + 6) = −x`. Any solution to *that* equation rides along.
Check `x = −2`: the left side `√4 = 2`, the right side is `−2`. The principal square root is never negative, so it fails — it solved the squared equation, not yours.
The rule: **any time you square both sides (or multiply by an expression containing the variable), checking in the original equation is part of solving, not optional.** Same idea applies to logarithmic equations, where solutions that make an argument ≤ 0 must be thrown out.