To find the equation that can be used to determine the possible values for the length of Gabby's backyard, let's define the variables:
- Let \( x \) be the length of the backyard (in meters).
- Since the width is 4 meters shorter than the length, the width can be expressed as \( x - 4 \) meters.
The area of a rectangle can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
According to the information provided, the area of Gabby's backyard is 120 square meters. Therefore, we can set up the equation as follows:
\[ x \cdot (x - 4) = 120 \]
This can be simplified or rearranged to:
\[ x^2 - 4x - 120 = 0 \]
Thus, the equation that can be used to find the possible values for the length \( x \) of Gabby's backyard is:
\[ x^2 - 4x - 120 = 0 \]
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