To solve the equation \( 0 = -\frac{1}{2}x(x - 20) \) using the Zero Product Property, we start by understanding that this property states that if a product of multiple factors equals zero, then at least one of the factors must be zero.
In this case, we have two factors in the equation:
- \(-\frac{1}{2}x\)
- \(x - 20\)
According to the Zero Product Property, we can set each factor equal to zero:
- \(-\frac{1}{2}x = 0\)
- \(x - 20 = 0\)
Now, we solve each equation separately.
For the first equation:
\[ -\frac{1}{2}x = 0 \]
To solve for \(x\), we can multiply both sides by \(-2\):
\[ x = 0 \]
For the second equation:
\[ x - 20 = 0 \]
Adding \(20\) to both sides gives:
\[ x = 20 \]
Now we have two solutions: \(x = 0\) and \(x = 20\).
The \(x = 0\) solution corresponds to the point when the ball is kicked (starting point), and \(x = 20\) corresponds to the point when the ball hits the ground.
Thus, the ball travels a horizontal distance of 20 units before it hits the ground.
In summary, the correct approach is to set the factors to zero and solve, leading us to the horizontal distances the ball has traveled when its height equals 0. The proper choice would be to "solve the two equations: \(-\frac{1}{2}x = 0\) and \(x - 20 = 0\)."