Solve for a
a=\sqrt{7}+4\approx 6.645751311
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a≔\sqrt{7}+4
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a=\frac{1}{2}\left(\left(\sqrt{7}\right)^{2}+2\sqrt{7}+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{7}+1\right)^{2}.
a=\frac{1}{2}\left(7+2\sqrt{7}+1\right)
The square of \sqrt{7} is 7.
a=\frac{1}{2}\left(8+2\sqrt{7}\right)
Add 7 and 1 to get 8.
a=4+\sqrt{7}
Use the distributive property to multiply \frac{1}{2} by 8+2\sqrt{7}.
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