Checking Solutions Math Example 2

Solution

1. 1
   Square both sides: $x + 3 = (x-3)^2 = x^2 - 6x + 9$.
2. 2
   Rearrange: $x^2 - 7x + 6 = 0$, factor: $(x-1)(x-6) = 0$.
3. 3
   Candidates: $x = 1$ and $x = 6$.
4. 4
   Check $x = 1$: $\sqrt{4} = 2$ but $1 - 3 = -2$. $2 \neq -2$ ✗ (extraneous).
5. 5
   Check $x = 6$: $\sqrt{9} = 3$ and $6 - 3 = 3$. $3 = 3$ ✓