Solve 1/4x^2+1/9=0

$$\frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 9 } = 0$$

Solve for x (complex solution)

$$x=-\frac{2}{3}i\approx -0.666666667i$$

$$x=\frac{2}{3}i\approx 0.666666667i$$

Steps by Finding Square Root

Subtract \frac{1}{9} from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{4}x^{2}=-\frac{1}{9}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x^{2}=-\frac{1}{9}\times 4$$

Multiply -\frac{1}{9} and 4 to get -\frac{4}{9}.

$$x^{2}=-\frac{4}{9}$$

The equation is now solved.

$$x=\frac{2}{3}i x=-\frac{2}{3}i$$

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.

$$\frac{1}{4}x^{2}+\frac{1}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{4} for a, 0 for b, and \frac{1}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{4}\times \frac{1}{9}}}{2\times \frac{1}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{4}\times \frac{1}{9}}}{2\times \frac{1}{4}}$$

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

$$x=\frac{0±\sqrt{-\frac{1}{9}}}{2\times \frac{1}{4}}$$

Take the square root of -\frac{1}{9}.

$$x=\frac{0±\frac{1}{3}i}{2\times \frac{1}{4}}$$

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

$$x=\frac{0±\frac{1}{3}i}{\frac{1}{2}}$$

Now solve the equation x=\frac{0±\frac{1}{3}i}{\frac{1}{2}} when ± is plus.

$$x=\frac{2}{3}i$$

Now solve the equation x=\frac{0±\frac{1}{3}i}{\frac{1}{2}} when ± is minus.

$$x=-\frac{2}{3}i$$

The equation is now solved.

$$x=\frac{2}{3}i x=-\frac{2}{3}i$$