To simplify the expression \( 2x^2 + 2x + 7(x + 7) \), follow these steps:
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Start by distributing the \(7\) in the term \(7(x + 7)\):
\[ 7(x + 7) = 7x + 49 \]
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Now substitute back into the original expression:
\[ 2x^2 + 2x + 7x + 49 \]
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Combine like terms:
- Combine \(2x\) and \(7x\):
\[ 2x + 7x = 9x \]
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The expression simplifies to:
\[ 2x^2 + 9x + 49 \]
So, the final simplified expression is:
\[ \boxed{2x^2 + 9x + 49} \]