1. The problem is to rewrite the expression for $x$ given by $$x=\frac{4(L+W)\pm \sqrt{[4(L+W)]^{2}-4(12)(LW)}}{2(12)}$$ into a proper, clear mathematical format. 2. This expression is a solution to a quadratic equation using the quadratic formula: $$x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=12$, $b=-4(L+W)$, and $c=LW$. 3. Notice the original formula has $4(L+W)$ in the numerator without a negative sign, but the quadratic formula requires $-b$, so $b$ should be $-4(L+W)$. 4. Rewrite the expression with correct signs: $$x=\frac{-4(L+W) \pm \sqrt{[4(L+W)]^{2} - 4 \times 12 \times LW}}{2 \times 12}$$ 5. Simplify the denominator: $$x=\frac{-4(L+W) \pm \sqrt{16(L+W)^2 - 48LW}}{24}$$ 6. This is the properly formatted and simplified expression for $x$. Final answer: $$x=\frac{-4(L+W) \pm \sqrt{16(L+W)^2 - 48LW}}{24}$$