Solve 1/2x^2-2=0

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

Solve for x

$$x=2$$

$$x=-2$$

Steps Using Difference of Squares

Multiply both sides by 2.

$$x^{2}-4=0$$

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

To find equation solutions, solve x-2=0 and x+2=0.

$$x=2 x=-2$$

Steps by Finding Square Root

Add 2 to both sides. Anything plus zero gives itself.

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

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

$$x^{2}=2\times 2$$

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}.

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

Square 0.

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

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

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

Multiply -2 times -2.

$$x=\frac{0±\sqrt{4}}{2\times \frac{1}{2}}$$

Take the square root of 4.

$$x=\frac{0±2}{2\times \frac{1}{2}}$$

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

$$x=\frac{0±2}{1}$$

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.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$