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0.5x^{2}=2
Add 2 to both sides. Anything plus zero gives itself.
x^{2}=\frac{2}{0.5}
Divide both sides by 0.5.
x^{2}=\frac{20}{5}
Expand \frac{2}{0.5} by multiplying both numerator and the denominator by 10.
x^{2}=4
Divide 20 by 5 to get 4.
x=2 x=-2
Take the square root of both sides of the equation.
0.5x^{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 0.5\left(-2\right)}}{2\times 0.5}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.5 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 0.5\left(-2\right)}}{2\times 0.5}
Square 0.
x=\frac{0±\sqrt{-2\left(-2\right)}}{2\times 0.5}
Multiply -4 times 0.5.
x=\frac{0±\sqrt{4}}{2\times 0.5}
Multiply -2 times -2.
x=\frac{0±2}{2\times 0.5}
Take the square root of 4.
x=\frac{0±2}{1}
Multiply 2 times 0.5.
x=2
Now solve the equation x=\frac{0±2}{1} when ± is plus.
x=-2
Now solve the equation x=\frac{0±2}{1} when ± is minus.
x=2 x=-2
The equation is now solved.