To determine how far the ball will have traveled when it hits the ground, we need to solve the equation:
\[ 0 = -130x(x - 61) \]
We can set this equation to zero by factoring. The equation is already factored as \( -130x(x - 61) \). Setting each factor equal to zero gives us two equations to solve:
- \( -130x = 0 \)
- \( x - 61 = 0 \)
Solving the first equation:
\[ -130x = 0 \implies x = 0 \]
Solving the second equation:
\[ x - 61 = 0 \implies x = 61 \]
The possible solutions for \( x \) are \( 0 \) and \( 61 \).
The solution \( x = 0 \) corresponds to the starting point of the kick. The solution \( x = 61 \) represents the horizontal distance the ball has traveled when it hits the ground.
Thus, the ball will have traveled 61 yards before hitting the ground.