Solve 1/2x^2-7=0

$$\frac { 1 } { 2 } x ^ { 2 } - 7 = 0$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Add 7 to both sides. Anything plus zero gives itself.

$$\frac{1}{2}x^{2}=7$$

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

$$x^{2}=7\times 2$$

Multiply 7 and 2 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

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.

$$\frac{1}{2}x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-7\right)}}{2\times \frac{1}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-7\right)}}{2\times \frac{1}{2}}$$

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

$$x=\frac{0±\sqrt{-2\left(-7\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -7.

$$x=\frac{0±\sqrt{14}}{2\times \frac{1}{2}}$$

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

$$x=\frac{0±\sqrt{14}}{1}$$

Now solve the equation x=\frac{0±\sqrt{14}}{1} when ± is plus.

$$x=\sqrt{14}$$

Now solve the equation x=\frac{0±\sqrt{14}}{1} when ± is minus.

$$x=-\sqrt{14}$$

The equation is now solved.

$$x=\sqrt{14} x=-\sqrt{14}$$