Radical Equations Math Example 2

Solution

1. 1
   Step 1: Square both sides: $2x + 1 = (x-1)^2 = x^2 - 2x + 1$.
2. 2
   Step 2: Rearrange: $0 = x^2 - 4x$, so $x(x - 4) = 0$. Solutions: $x = 0$ or $x = 4$.
3. 3
   Step 3: Check $x = 0$: $\sqrt{1} = 1$ but $0 - 1 = -1$. $1 \neq -1$. Extraneous! ✗
4. 4
   Step 4: Check $x = 4$: $\sqrt{9} = 3$ and $4 - 1 = 3$. ✓