\( \Sigma ( x + 2 ) ^ { 2 } = 480 \)

To solve \( \Sigma ( x + 2 ) ^ { 2 } = 480 \), let's expand \( (x + 2)^2 \) first. This gives us \( x^2 + 4x + 4 \). Now, summing this expression over a certain number of terms means you are summing up the quadratic from a specific starting point to \( n \). Assuming you're summing from \( x = 1 \) to \( n \), you could use the formula for the sum of squares and the sum of integers. But, since you've set this equal to 480, we actually need to find values of \( x \) such that the cumulative total equals 480! You can also rearrange it into a more workable form: 1. Determine how many terms are involved \( n \). 2. Solve for \( n \) using the area or summation formulas. This brings you closer to finding \( x \) that meets this equation! Let’s crunch some numbers!