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x^{2}+x^{2}=2
Add x^{2} to both sides.
2x^{2}=2
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-2=0
Subtract 2 from both sides.
x^{2}-1=0
Divide both sides by 2.
\left(x-1\right)\left(x+1\right)=0
Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=1 x=-1
To find equation solutions, solve x-1=0 and x+1=0.
x^{2}+x^{2}=2
Add x^{2} to both sides.
2x^{2}=2
Combine x^{2} and x^{2} to get 2x^{2}.
x^{2}=\frac{2}{2}
Divide both sides by 2.
x^{2}=1
Divide 2 by 2 to get 1.
x=1 x=-1
Take the square root of both sides of the equation.
x^{2}+x^{2}=2
Add x^{2} to both sides.
2x^{2}=2
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-2=0
Subtract 2 from both sides.
x=\frac{0±\sqrt{0^{2}-4\times 2\left(-2\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 2\left(-2\right)}}{2\times 2}
Square 0.
x=\frac{0±\sqrt{-8\left(-2\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{0±\sqrt{16}}{2\times 2}
Multiply -8 times -2.
x=\frac{0±4}{2\times 2}
Take the square root of 16.
x=\frac{0±4}{4}
Multiply 2 times 2.
x=1
Now solve the equation x=\frac{0±4}{4} when ± is plus. Divide 4 by 4.
x=-1
Now solve the equation x=\frac{0±4}{4} when ± is minus. Divide -4 by 4.
x=1 x=-1
The equation is now solved.