Solve 9x^2+361x^2+1=0

$$9 { x }^{ 2 } +361 { x }^{ 2 } +1=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{370}i}{370}\approx -0-0.051987524i$$

$$x=\frac{\sqrt{370}i}{370}\approx 0.051987524i$$

Steps by Finding Square Root

Combine 9x^{2} and 361x^{2} to get 370x^{2}.

$$370x^{2}+1=0$$

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

$$370x^{2}=-1$$

Divide both sides by 370.

$$x^{2}=-\frac{1}{370}$$

The equation is now solved.

$$x=\frac{\sqrt{370}i}{370} x=-\frac{\sqrt{370}i}{370}$$

Steps Using the Quadratic Formula

Combine 9x^{2} and 361x^{2} to get 370x^{2}.

$$370x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 370 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 370}}{2\times 370}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 370}}{2\times 370}$$

Multiply -4 times 370.

$$x=\frac{0±\sqrt{-1480}}{2\times 370}$$

Take the square root of -1480.

$$x=\frac{0±2\sqrt{370}i}{2\times 370}$$

Multiply 2 times 370.

$$x=\frac{0±2\sqrt{370}i}{740}$$

Now solve the equation x=\frac{0±2\sqrt{370}i}{740} when ± is plus.

$$x=\frac{\sqrt{370}i}{370}$$

Now solve the equation x=\frac{0±2\sqrt{370}i}{740} when ± is minus.

$$x=-\frac{\sqrt{370}i}{370}$$

The equation is now solved.

$$x=\frac{\sqrt{370}i}{370} x=-\frac{\sqrt{370}i}{370}$$