Let's simplify the equation \(x^2 - 2x + 2 - 3x - x^2 = 0\).
First, combine like terms:
\[ x^2 - x^2 - 2x - 3x + 2 = 0 \]
This simplifies to:
\[ -5x + 2 = 0 \]
Now, isolate \(x\):
\[ -5x = -2 \]
Dividing both sides by -5 gives:
\[ x = \frac{2}{5} \]
Since this is a linear equation, there is only one solution. Thus, the larger \(x\) value does not exist.
Therefore, the answer is:
\(x = \frac{2}{5}\) and blank for the second box.