An algebra problem by Cj Lagmay

Algebra Level 4

\[ \sqrt{x} + 2 \sqrt{x^{2} + 7x} + \sqrt{x + 7} = 35 - 2x\]

The real solution to the above equation is of the form \( \frac{a}{b} \), where \(a\) and \(b\) are positive coprime integers. What is \(a + b \)?

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