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2=x\times 2x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.
2=x^{2}\times 2
Multiply x and x to get x^{2}.
x^{2}\times 2=2
Swap sides so that all variable terms are on the left hand side.
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.
2=x\times 2x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.
2=x^{2}\times 2
Multiply x and x to get x^{2}.
x^{2}\times 2=2
Swap sides so that all variable terms are on the left hand side.
x^{2}\times 2-2=0
Subtract 2 from both sides.
2x^{2}-2=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
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.