Let's work through the problem step-by-step to determine the correct equation to solve for [tex]\(x\)[/tex], the side length of the original square piece of paper.
1. Determine the area of the original square piece of paper:
- The area of a square is given by the square of its side length.
- So, the area of the square is [tex]\(x^2\)[/tex] square units.
2. Determine the area of the rectangular strip that is cut off:
- The rectangular strip has a width of 2 units and a length of [tex]\(x\)[/tex] units.
- The area of the strip is calculated as width multiplied by length.
- Therefore, the area of the rectangular strip is [tex]\(2 \times x = 2x\)[/tex] square units.
3. Determine the remaining area of the paper after cutting off the rectangular strip:
- The remaining area is given as 120 square units.
4. Formulate the equation:
- The original area of the square minus the area of the rectangular strip equals the remaining area.
- This can be written as: [tex]\(x^2 - 2x = 120\)[/tex].
5. Rearrange the equation to standard form (quadratic equation):
- To get the equation in the standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex], we move all terms to one side of the equation.
- Thus, [tex]\(x^2 - 2x - 120 = 0\)[/tex].
So, the correct equation to solve for [tex]\(x\)[/tex] is:
[tex]\[ x^2 - 2x - 120 = 0 \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{x^2 - 2x - 120 = 0} \][/tex]
