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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