Solve 118x^2=-1

$$118 x ^ { 2 } = - 1$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{118}i}{118}\approx -0-0.092057462i$$

$$x=\frac{\sqrt{118}i}{118}\approx 0.092057462i$$

Steps by Finding Square Root

Divide both sides by 118.

$$x^{2}=-\frac{1}{118}$$

The equation is now solved.

$$x=\frac{\sqrt{118}i}{118} x=-\frac{\sqrt{118}i}{118}$$

Steps Using the Quadratic Formula

Divide both sides by 118.

$$x^{2}=-\frac{1}{118}$$

Add \frac{1}{118} to both sides.

$$x^{2}+\frac{1}{118}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{1}{118} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{118}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{118}}}{2}$$

Multiply -4 times \frac{1}{118}.

$$x=\frac{0±\sqrt{-\frac{2}{59}}}{2}$$

Take the square root of -\frac{2}{59}.

$$x=\frac{0±\frac{\sqrt{118}i}{59}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{118}i}{59}}{2} when ± is plus.

$$x=\frac{\sqrt{118}i}{118}$$

Now solve the equation x=\frac{0±\frac{\sqrt{118}i}{59}}{2} when ± is minus.

$$x=-\frac{\sqrt{118}i}{118}$$

The equation is now solved.

$$x=\frac{\sqrt{118}i}{118} x=-\frac{\sqrt{118}i}{118}$$