Solve (x+2)² - 12 = x²: Perfect Square Equation Challenge

Let's examine the given equation:

$(x+2)^2-12=x^2$First, let's simplify the equation, for this we'll use the perfect square binomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$,

We'll start by opening the parentheses on the left side using the perfect square formula and then move terms and combine like terms, in the final step we'll solve the simplified equation we get:

$(x+2)^2-12=x^2 \\ \downarrow\\ x^2+2\cdot x\cdot2+2^2-12=x^2\\ x^2+4x+4-12= x^2\\ 4x=8\hspace{6pt}\text{/}:4\\ \boxed{x=2}$Therefore, the correct answer is answer C.