Solve 4/x^2+45=0

$$\frac{ 4 }{ { x }^{ 2 } } +45=0$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{5}i}{15}\approx -0-0.298142397i$$

$$x=\frac{2\sqrt{5}i}{15}\approx 0.298142397i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$4+x^{2}\times 45=0$$

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

$$x^{2}\times 45=-4$$

Divide both sides by 45.

$$x^{2}=-\frac{4}{45}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}i}{15} x=-\frac{2\sqrt{5}i}{15}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$4+x^{2}\times 45=0$$

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.

$$45x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 45 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 45\times 4}}{2\times 45}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 45\times 4}}{2\times 45}$$

Multiply -4 times 45.

$$x=\frac{0±\sqrt{-180\times 4}}{2\times 45}$$

Multiply -180 times 4.

$$x=\frac{0±\sqrt{-720}}{2\times 45}$$

Take the square root of -720.

$$x=\frac{0±12\sqrt{5}i}{2\times 45}$$

Multiply 2 times 45.

$$x=\frac{0±12\sqrt{5}i}{90}$$

Now solve the equation x=\frac{0±12\sqrt{5}i}{90} when ± is plus.

$$x=\frac{2\sqrt{5}i}{15}$$

Now solve the equation x=\frac{0±12\sqrt{5}i}{90} when ± is minus.

$$x=-\frac{2\sqrt{5}i}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}i}{15} x=-\frac{2\sqrt{5}i}{15}$$