Solve for x
x=2\sqrt{2}\approx 2.828427125
x=-2\sqrt{2}\approx -2.828427125
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2x^{2}=16
Combine x^{2} and x^{2} to get 2x^{2}.
x^{2}=\frac{16}{2}
Divide both sides by 2.
x^{2}=8
Divide 16 by 2 to get 8.
x=2\sqrt{2} x=-2\sqrt{2}
Take the square root of both sides of the equation.
2x^{2}=16
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-16=0
Subtract 16 from both sides.
x=\frac{0±\sqrt{0^{2}-4\times 2\left(-16\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 2\left(-16\right)}}{2\times 2}
Square 0.
x=\frac{0±\sqrt{-8\left(-16\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{0±\sqrt{128}}{2\times 2}
Multiply -8 times -16.
x=\frac{0±8\sqrt{2}}{2\times 2}
Take the square root of 128.
x=\frac{0±8\sqrt{2}}{4}
Multiply 2 times 2.
x=2\sqrt{2}
Now solve the equation x=\frac{0±8\sqrt{2}}{4} when ± is plus.
x=-2\sqrt{2}
Now solve the equation x=\frac{0±8\sqrt{2}}{4} when ± is minus.
x=2\sqrt{2} x=-2\sqrt{2}
The equation is now solved.
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