### Instruction: What is the value of $x$ for which $(8-x)^2=x^2$?### Response: I want to solve for $x$, so I need to get rid of the parentheses and simplify the equation.
I can use the square of a binomial formula to expand $(8-x)^2$ as $64-16x+x^2$.
Then I have $64-16x+x^2=x^2$.
I can subtract $x^2$ from both sides and get $64-16x=0$.
Now I can add $16x$ to both sides and get $64=16x$.
To isolate $x$, I can divide both sides by $16$ and get $x=4$.
I can check my answer by plugging it back into the original equation and seeing if it makes it true.
I have $(8-4)^2=4^2$, which simplifies to $16=16$, which is true.