Step 1: Expand both squared expressions on both sides of the equation.
(x + 1)^2 = x^2 + 2x + 1
(x + 2)^2 = x^2 + 4x + 4
Step 2: Substitute these expansions back into the equation.
x^2 + 2x + 1 = x^2 + 4x + 4 - 2(x + 1)
Step 3: Distribute the -2 on the right-hand side.
x^2 + 2x + 1 = x^2 + 4x + 4 - 2x - 2
Step 4: Combine like terms on the right-hand side.
x^2 + 2x + 1 = x^2 + 2x + 2
Step 5: Cancel out x^2 + 2x from both sides.
1 = 2 \quad \text{(False)}
So, x doesn't necessarily.