The problem asks us to simplify the given expression by combining like terms: $-3x + x^2 + 9 - x^2 + 2x - 7$.

1. Problem Description

The problem asks us to simplify the given expression by combining like terms: $-3x + x^2 + 9 - x^2 + 2x - 7$.

2. Solution Steps

We need to identify the like terms and combine them. Like terms are terms that have the same variable raised to the same power.

* Terms with $x^2$: $x^2$ and $-x^2$. Their combination is $x^2 - x^2 = 0x^2 = 0$.

* Terms with $x$: $-3x$ and $2x$. Their combination is $-3x + 2x = -1x = -x$.

* Constant terms: $9$ and $-7$. Their combination is $9 - 7 = 2$.

Combining all these results, the simplified expression is $0 - x + 2 = -x + 2$.

3. Final Answer

$-x + 2$