Solve for a
a=\frac{\sqrt{2}}{2}\approx 0.707106781
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\left(2+\sqrt{2}\right)a=\sqrt{2}+1
Combine all terms containing a.
\left(\sqrt{2}+2\right)a=\sqrt{2}+1
The equation is in standard form.
\frac{\left(\sqrt{2}+2\right)a}{\sqrt{2}+2}=\frac{\sqrt{2}+1}{\sqrt{2}+2}
Divide both sides by 2+\sqrt{2}.
a=\frac{\sqrt{2}+1}{\sqrt{2}+2}
Dividing by 2+\sqrt{2} undoes the multiplication by 2+\sqrt{2}.
a=\frac{\sqrt{2}}{2}
Divide \sqrt{2}+1 by 2+\sqrt{2}.
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