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2\times 4x^{2}\sqrt{4}-2=0
Multiply x and x to get x^{2}.
8x^{2}\sqrt{4}-2=0
Multiply 2 and 4 to get 8.
8x^{2}\times 2-2=0
Calculate the square root of 4 and get 2.
16x^{2}-2=0
Multiply 8 and 2 to get 16.
16x^{2}=2
Add 2 to both sides. Anything plus zero gives itself.
x^{2}=\frac{2}{16}
Divide both sides by 16.
x^{2}=\frac{1}{8}
Reduce the fraction \frac{2}{16} to lowest terms by extracting and canceling out 2.
x=\frac{\sqrt{2}}{4} x=-\frac{\sqrt{2}}{4}
Take the square root of both sides of the equation.
2\times 4x^{2}\sqrt{4}-2=0
Multiply x and x to get x^{2}.
8x^{2}\sqrt{4}-2=0
Multiply 2 and 4 to get 8.
8x^{2}\times 2-2=0
Calculate the square root of 4 and get 2.
16x^{2}-2=0
Multiply 8 and 2 to get 16.
x=\frac{0±\sqrt{0^{2}-4\times 16\left(-2\right)}}{2\times 16}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 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 16\left(-2\right)}}{2\times 16}
Square 0.
x=\frac{0±\sqrt{-64\left(-2\right)}}{2\times 16}
Multiply -4 times 16.
x=\frac{0±\sqrt{128}}{2\times 16}
Multiply -64 times -2.
x=\frac{0±8\sqrt{2}}{2\times 16}
Take the square root of 128.
x=\frac{0±8\sqrt{2}}{32}
Multiply 2 times 16.
x=\frac{\sqrt{2}}{4}
Now solve the equation x=\frac{0±8\sqrt{2}}{32} when ± is plus.
x=-\frac{\sqrt{2}}{4}
Now solve the equation x=\frac{0±8\sqrt{2}}{32} when ± is minus.
x=\frac{\sqrt{2}}{4} x=-\frac{\sqrt{2}}{4}
The equation is now solved.