Solve for X: (x+2)² = x² + 12 Perfect Square Equation

Solve for x:

$(x+2)^2=x^2+12$

Let's solve the equation. First, we'll simplify the algebraic expressions using the perfect square binomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$We'll then apply the mentioned formula and expand the parentheses in the expression in the equation:

$(x+2)^2=x^2+12 \\ x^2+2\cdot x\cdot2+2^2=x^2+12\\ x^2+4x+4=x^2+12$We'll continue and combine like terms, by moving terms around. Later - we can notice that the squared term cancels out, therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$x^2+4x+4=x^2+12 \\ 4x=8\hspace{8pt}\text{/}:4\\ \boxed{x=2}$Therefore, the correct answer is answer C.