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\left(4+\sqrt{2}\right)x=1
Combine all terms containing x.
\left(\sqrt{2}+4\right)x=1
The equation is in standard form.
\frac{\left(\sqrt{2}+4\right)x}{\sqrt{2}+4}=\frac{1}{\sqrt{2}+4}
Divide both sides by 4+\sqrt{2}.
x=\frac{1}{\sqrt{2}+4}
Dividing by 4+\sqrt{2} undoes the multiplication by 4+\sqrt{2}.
x=-\frac{\sqrt{2}}{14}+\frac{2}{7}
Divide 1 by 4+\sqrt{2}.