(x + 1)2 = (x + 2)2 — 2(x + 1)

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.