Solve the Quadratic Equation: (x-4)² - x(x+8) = 0

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 apply the mentioned formula and expand the parentheses in the expressions in the equation:

$(x-4)^2-x(x+8)=0 \\ x^2-2\cdot x\cdot4+4^2-x^2-8x=0 \\ x^2-8x+16-x^2-8x=0$In the first stage, we used the distributive property to expand the parentheses,

We'll continue and combine like terms, by moving terms between sides. Then - we can notice that the squared term cancels out and 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:

$x^2-8x+16-x^2-8x=0 \\ -16x=-16\hspace{8pt}\text{/}:(-16)\\ \boxed{x=1}$Therefore, the correct answer is answer D.