Solve the Quadratic Equation: x²-8x+16=0 Using Perfect Square Method

Let's solve the given equation:

$x^2-8x+16=0$We identify that we can factor the expression on the left side using the perfect square trinomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$Let's do this:

$x^2-8x+16=0 \\ x^2\textcolor{blue}{-8x}+4^2=0 \\ x^2\textcolor{blue}{-2\cdot x\cdot4}+4^2=0 \\ \downarrow\\ (x-4)^2=0$Note that factoring using this formula was only possible because the middle term in the expression (which is in first power in this case and highlighted in blue in the previous calculation) indeed matched the middle term in the perfect square trinomial formula,

We'll continue and solve the resulting equation by taking the square root of both sides:

$(x-4)^2=0 \hspace{6pt}\text{/}\sqrt{\hspace{4pt}}\\ x-4=0\\ \boxed{x=4}$Therefore, the correct answer is answer C.