Solve 1/2x^2-4=0

$$\frac { 1 } { 2 } x ^ { 2 } - 4 = 0$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Add 4 to both sides. Anything plus zero gives itself.

$$\frac{1}{2}x^{2}=4$$

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

$$x^{2}=4\times 2$$

Multiply 4 and 2 to get 8.

$$x^{2}=8$$

Take the square root of both sides of the equation.

$$x=2\sqrt{2} x=-2\sqrt{2}$$

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.

$$\frac{1}{2}x^{2}-4=0$$

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

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

Square 0.

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

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

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

Multiply -2 times -4.

$$x=\frac{0±\sqrt{8}}{2\times \frac{1}{2}}$$

Take the square root of 8.

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

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

$$x=\frac{0±2\sqrt{2}}{1}$$

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

$$x=2\sqrt{2}$$

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

$$x=-2\sqrt{2}$$

The equation is now solved.

$$x=2\sqrt{2} x=-2\sqrt{2}$$