To perform the operation \((-7x^2 + 3x - 10) + (-6x^2 - 10x + 3)\), we combine like terms.
Here are the terms grouped by their degrees:
- Quadratic terms: \(-7x^2\) and \(-6x^2\)
- Linear terms: \(3x\) and \(-10x\)
- Constant terms: \(-10\) and \(3\)
Now, we combine these:
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For the quadratic terms: \[ -7x^2 - 6x^2 = -13x^2 \]
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For the linear terms: \[ 3x - 10x = -7x \]
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For the constant terms: \[ -10 + 3 = -7 \]
Now we can put all the combined terms together:
\[ -13x^2 - 7x - 7 \]
Thus, the result of the operation is: \[ \boxed{-13x^2 - 7x - 7} \]
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