Solve 1/2x^2+7=0

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

Solve for x (complex solution)

$$x=-\sqrt{14}i\approx -0-3.741657387i$$

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

Steps by Finding Square Root

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

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

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

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

Multiply -7 and 2 to get -14.

$$x^{2}=-14$$

The equation is now solved.

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

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}.

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

Square 0.

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

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

$$x=\frac{0±\sqrt{-2\times 7}}{2\times \frac{1}{2}}$$

Multiply -2 times 7.

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

Take the square root of -14.

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

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

$$x=\frac{0±\sqrt{14}i}{1}$$

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

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

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

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

The equation is now solved.

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