To solve the equation \( 0 = -\frac{1}{2}x(x - 20) \) using the zero product property, we first recognize that this property states if a product of factors equals zero, then at least one of the factors must be zero.
Given the equation:
\[ 0 = -\frac{1}{2}x(x - 20) \]
we can set the factors equal to zero. First, ignore the \(-\frac{1}{2}\) since it doesn't affect the zero equality:
\[ x(x - 20) = 0 \]
Now we can apply the zero product property:
- Set each factor equal to zero:
- \( x = 0 \)
- \( x - 20 = 0 \) → \( x = 20 \)
Thus, the solutions to the equation are:
\[ x = 0 \quad \text{and} \quad x = 20 \]
In this context, \(x\) represents the horizontal distance traveled by the ball. The solutions indicate that:
- When \(x = 0\), it is at the initial position (the starting point, where the ball was kicked).
- When \(x = 20\), it is the horizontal distance traveled when the height of the soccer ball is zero (when the ball hits the ground).
Therefore, the horizontal distance the ball has traveled when the height equals zero is 20 units.