Solve -4x^2=1/4

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

Solve for x (complex solution)

$$x=-\frac{1}{4}i=-0.25i$$

$$x=\frac{1}{4}i=0.25i$$

Steps by Finding Square Root

Divide both sides by -4.

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

Express \frac{\frac{1}{4}}{-4} as a single fraction.

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

Multiply 4 and -4 to get -16.

$$x^{2}=\frac{1}{-16}$$

Fraction \frac{1}{-16} can be rewritten as -\frac{1}{16} by extracting the negative sign.

$$x^{2}=-\frac{1}{16}$$

The equation is now solved.

$$x=\frac{1}{4}i x=-\frac{1}{4}i$$

Steps Using the Quadratic Formula

Divide both sides by -4.

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

Express \frac{\frac{1}{4}}{-4} as a single fraction.

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

Multiply 4 and -4 to get -16.

$$x^{2}=\frac{1}{-16}$$

Fraction \frac{1}{-16} can be rewritten as -\frac{1}{16} by extracting the negative sign.

$$x^{2}=-\frac{1}{16}$$

Add \frac{1}{16} to both sides.

$$x^{2}+\frac{1}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{1}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{16}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{16}}}{2}$$

Multiply -4 times \frac{1}{16}.

$$x=\frac{0±\sqrt{-\frac{1}{4}}}{2}$$

Take the square root of -\frac{1}{4}.

$$x=\frac{0±\frac{1}{2}i}{2}$$

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

$$x=\frac{1}{4}i$$

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

$$x=-\frac{1}{4}i$$

The equation is now solved.

$$x=\frac{1}{4}i x=-\frac{1}{4}i$$