To solve for [tex]\( x \)[/tex], the side length of the original square piece of paper, given the conditions in the problem, we need to set up an equation based on the information provided:
1. The area of the original square is [tex]\( x^2 \)[/tex] square units.
2. A rectangular strip with dimensions 2 units (width) by [tex]\( x \)[/tex] units (length) is cut off from the square. The area of this rectangular strip is therefore [tex]\( 2 \times x = 2x \)[/tex] square units.
3. After cutting off the rectangular strip, the remaining area of the paper is 120 square units.
We can write this relationship as:
[tex]\[ \text{Original area} - \text{Area of the rectangular strip} = \text{Remaining area} \][/tex]
Substituting the known values:
[tex]\[ x^2 - 2x = 120 \][/tex]
To form a standard quadratic equation, we rearrange this to equal zero:
[tex]\[ x^2 - 2x - 120 = 0 \][/tex]
Therefore, the equation that can be used to solve for [tex]\( x \)[/tex] is:
[tex]\[ x^2 - 2x - 120 = 0 \][/tex]
The correct answer is:
[tex]\[ x^2 - 2x - 120 = 0 \][/tex]
