1. **State the problem:** We are given the equation $$2x^2 - 2x = 112$$ and need to find which of the provided options is equivalent to it. 2. **Rewrite the equation in standard form:** To compare with the options, we move all terms to one side to set the equation equal to zero. 3. Subtract 112 from both sides: $$2x^2 - 2x - 112 = 112 - 112$$ 4. Simplify the right side: $$2x^2 - 2x - 112 = 0$$ 5. This matches option 2 exactly. **Final answer:** Option 2) $$2x^2 - 2x - 112 = 0$$