Solve x^2=-40/41

$$x ^ { 2 } = - \frac { 40 } { 41 }$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{410}i}{41}\approx -0-0.987729597i$$

$$x=\frac{2\sqrt{410}i}{41}\approx 0.987729597i$$

Steps by Finding Square Root

The equation is now solved.

$$x=\frac{2\sqrt{410}i}{41} x=-\frac{2\sqrt{410}i}{41}$$

Steps Using the Quadratic Formula

Add \frac{40}{41} to both sides.

$$x^{2}+\frac{40}{41}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{40}{41} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{40}{41}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{40}{41}}}{2}$$

Multiply -4 times \frac{40}{41}.

$$x=\frac{0±\sqrt{-\frac{160}{41}}}{2}$$

Take the square root of -\frac{160}{41}.

$$x=\frac{0±\frac{4\sqrt{410}i}{41}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{410}i}{41}}{2} when ± is plus.

$$x=\frac{2\sqrt{410}i}{41}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{410}i}{41}}{2} when ± is minus.

$$x=-\frac{2\sqrt{410}i}{41}$$

The equation is now solved.

$$x=\frac{2\sqrt{410}i}{41} x=-\frac{2\sqrt{410}i}{41}$$