A football field is 30 meters longer than it is wide, and its area is 7000 square meters. We need to find the mathematical expression that gives the solution to the problem. The width is represented by $x$ and the length is represented by $x+30$. The area of a rectangle is given by the formula $A = length \times width$.

1. Problem Description

A football field is 30 meters longer than it is wide, and its area is 7000 square meters. We need to find the mathematical expression that gives the solution to the problem. The width is represented by $x$ and the length is represented by $x+30$. The area of a rectangle is given by the formula $A = length \times width$.

2. Solution Steps

The area of the football field is given as 7000 square meters.

The length of the field is $x+30$ and the width is $x$.

Therefore, we can write the equation for the area as:

$A = (x+30)x$

We know that $A = 7000$, so we can substitute this into the equation:

$7000 = (x+30)x$

Now, expand the equation:

$7000 = x^2 + 30x$

To get the equation in the standard form of a quadratic equation, subtract 7000 from both sides:

$x^2 + 30x - 7000 = 0$

3. Final Answer

The correct equation is $x^2 + 30x - 7000 = 0$.

So, the answer is a. $x^2 + 30x - 7000 = 0$.