Solve 20/x^2+4+4/1=0

$$\frac { 20 } { x ^ { 2 } + 4 } + \frac { 4 } { 1 } = 0$$

Solve for x (complex solution)

$$x=-3i$$

$$x=3i$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -2i,2i since division by zero is not defined. Multiply both sides of the equation by \left(x-2i\right)\left(x+2i\right).

$$20+\left(x^{2}+4\right)\times 4=0$$

Use the distributive property to multiply x^{2}+4 by 4.

$$20+4x^{2}+16=0$$

Add 20 and 16 to get 36.

$$36+4x^{2}=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$4x^{2}=-36$$

Divide both sides by 4.

$$x^{2}=\frac{-36}{4}$$

Divide -36 by 4 to get -9.

$$x^{2}=-9$$

The equation is now solved.

$$x=3i x=-3i$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -2i,2i since division by zero is not defined. Multiply both sides of the equation by \left(x-2i\right)\left(x+2i\right).

$$20+\left(x^{2}+4\right)\times 4=0$$

Use the distributive property to multiply x^{2}+4 by 4.

$$20+4x^{2}+16=0$$

Add 20 and 16 to get 36.

$$36+4x^{2}=0$$

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.

$$4x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 36}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 36}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 36}}{2\times 4}$$

Multiply -16 times 36.

$$x=\frac{0±\sqrt{-576}}{2\times 4}$$

Take the square root of -576.

$$x=\frac{0±24i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±24i}{8}$$

Now solve the equation x=\frac{0±24i}{8} when ± is plus.

$$x=3i$$

Now solve the equation x=\frac{0±24i}{8} when ± is minus.

$$x=-3i$$

The equation is now solved.

$$x=3i x=-3i$$