To find the sum of the two expressions \( (7x^2 - 6x + 2) + (-5x + 10x - 9) \), we first simplify the expression inside the second set of parentheses.
- Combine the terms in the second expression: \[ -5x + 10x - 9 = (10x - 5x) - 9 = 5x - 9 \]
Now, rewrite the original expression with the simplified second term: \[ (7x^2 - 6x + 2) + (5x - 9) \]
- Now, combine like terms:
- \(7x^2\) (there is no other \(x^2\) term)
- For the \(x\) terms: \(-6x + 5x = -x\)
- For the constant terms: \(2 - 9 = -7\)
Putting it all together: \[ 7x^2 - x - 7 \]
The final result of the expression \( (7x^2 - 6x + 2) + (-5x + 10x - 9) \) is: \[ \boxed{7x^2 - x - 7} \]
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