MHB Solving an Equation to find the value of x

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Calculate value of $x$ in $\displaystyle \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+x}}}} = x$
 
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Hint: let $\displaystyle x+1=x^2$
 
Good morning I have been refreshing my memory about Leibniz differentiation of integrals and found some useful videos from digital-university.org on YouTube. Although the audio quality is poor and the speaker proceeds a bit slowly, the explanations and processes are clear. However, it seems that one video in the Leibniz rule series is missing. While the videos are still present on YouTube, the referring website no longer exists but is preserved on the internet archive...

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