Solve -1/2x^2+2=0

$$- \frac{ 1 }{ 2 } { x }^{ 2 } +2 = 0$$

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{2}x^{2}=-2$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x^{2}=-2\left(-2\right)$$

Multiply -2 and -2 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

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.

$$-\frac{1}{2}x^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{2} for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{2}\right)\times 2}}{2\left(-\frac{1}{2}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{2}\right)\times 2}}{2\left(-\frac{1}{2}\right)}$$

Multiply -4 times -\frac{1}{2}.

$$x=\frac{0±\sqrt{2\times 2}}{2\left(-\frac{1}{2}\right)}$$

Multiply 2 times 2.

$$x=\frac{0±\sqrt{4}}{2\left(-\frac{1}{2}\right)}$$

Take the square root of 4.

$$x=\frac{0±2}{2\left(-\frac{1}{2}\right)}$$

Multiply 2 times -\frac{1}{2}.

$$x=\frac{0±2}{-1}$$

Now solve the equation x=\frac{0±2}{-1} when ± is plus. Divide 2 by -1.

$$x=-2$$

Now solve the equation x=\frac{0±2}{-1} when ± is minus. Divide -2 by -1.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$