Solve 1/x^2+365+8=0

$$\frac { 1 } { x ^ { 2 } } + 365 + 8 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{373}i}{373}\approx -0-0.051778037i$$

$$x=\frac{\sqrt{373}i}{373}\approx 0.051778037i$$

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}.

$$1+x^{2}\times 365+x^{2}\times 8=0$$

Combine x^{2}\times 365 and x^{2}\times 8 to get 373x^{2}.

$$1+373x^{2}=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$373x^{2}=-1$$

Divide both sides by 373.

$$x^{2}=-\frac{1}{373}$$

The equation is now solved.

$$x=\frac{\sqrt{373}i}{373} x=-\frac{\sqrt{373}i}{373}$$

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}.

$$1+x^{2}\times 365+x^{2}\times 8=0$$

Combine x^{2}\times 365 and x^{2}\times 8 to get 373x^{2}.

$$1+373x^{2}=0$$

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.

$$373x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 373 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 373}}{2\times 373}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 373}}{2\times 373}$$

Multiply -4 times 373.

$$x=\frac{0±\sqrt{-1492}}{2\times 373}$$

Take the square root of -1492.

$$x=\frac{0±2\sqrt{373}i}{2\times 373}$$

Multiply 2 times 373.

$$x=\frac{0±2\sqrt{373}i}{746}$$

Now solve the equation x=\frac{0±2\sqrt{373}i}{746} when ± is plus.

$$x=\frac{\sqrt{373}i}{373}$$

Now solve the equation x=\frac{0±2\sqrt{373}i}{746} when ± is minus.

$$x=-\frac{\sqrt{373}i}{373}$$

The equation is now solved.

$$x=\frac{\sqrt{373}i}{373} x=-\frac{\sqrt{373}i}{373}$$