Solve 16x^2+4=0

$$16 x ^ { 2 } + 4 = 0$$

Solve for x (complex solution)

$$x=-\frac{1}{2}i=-0.5i$$

$$x=\frac{1}{2}i=0.5i$$

Steps by Finding Square Root

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$16x^{2}=-4$$

Divide both sides by 16.

$$x^{2}=\frac{-4}{16}$$

Reduce the fraction \frac{-4}{16} to lowest terms by extracting and canceling out 4.

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

The equation is now solved.

$$x=\frac{1}{2}i x=-\frac{1}{2}i$$

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.

$$16x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\times 4}}{2\times 16}$$

Multiply -64 times 4.

$$x=\frac{0±\sqrt{-256}}{2\times 16}$$

Take the square root of -256.

$$x=\frac{0±16i}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±16i}{32}$$

Now solve the equation x=\frac{0±16i}{32} when ± is plus.

$$x=\frac{1}{2}i$$

Now solve the equation x=\frac{0±16i}{32} when ± is minus.

$$x=-\frac{1}{2}i$$

The equation is now solved.

$$x=\frac{1}{2}i x=-\frac{1}{2}i$$