Solve for x
x=\sqrt{2}+1\approx 2.414213562
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1+x-\sqrt{2}x=0
Subtract \sqrt{2}x from both sides.
x-\sqrt{2}x=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
\left(1-\sqrt{2}\right)x=-1
Combine all terms containing x.
\frac{\left(1-\sqrt{2}\right)x}{1-\sqrt{2}}=-\frac{1}{1-\sqrt{2}}
Divide both sides by 1-\sqrt{2}.
x=-\frac{1}{1-\sqrt{2}}
Dividing by 1-\sqrt{2} undoes the multiplication by 1-\sqrt{2}.
x=\sqrt{2}+1
Divide -1 by 1-\sqrt{2}.
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