Solve x^2-41x^2-3=0

$$x ^ { 2 } - 41 x ^ { 2 } - 3 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30}i}{20}\approx -0-0.273861279i$$

$$x=\frac{\sqrt{30}i}{20}\approx 0.273861279i$$

Steps by Finding Square Root

Combine x^{2} and -41x^{2} to get -40x^{2}.

$$-40x^{2}-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$-40x^{2}=3$$

Divide both sides by -40.

$$x^{2}=-\frac{3}{40}$$

The equation is now solved.

$$x=\frac{\sqrt{30}i}{20} x=-\frac{\sqrt{30}i}{20}$$

Steps Using the Quadratic Formula

Combine x^{2} and -41x^{2} to get -40x^{2}.

$$-40x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -40 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-40\right)\left(-3\right)}}{2\left(-40\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-40\right)\left(-3\right)}}{2\left(-40\right)}$$

Multiply -4 times -40.

$$x=\frac{0±\sqrt{160\left(-3\right)}}{2\left(-40\right)}$$

Multiply 160 times -3.

$$x=\frac{0±\sqrt{-480}}{2\left(-40\right)}$$

Take the square root of -480.

$$x=\frac{0±4\sqrt{30}i}{2\left(-40\right)}$$

Multiply 2 times -40.

$$x=\frac{0±4\sqrt{30}i}{-80}$$

Now solve the equation x=\frac{0±4\sqrt{30}i}{-80} when ± is plus.

$$x=-\frac{\sqrt{30}i}{20}$$

Now solve the equation x=\frac{0±4\sqrt{30}i}{-80} when ± is minus.

$$x=\frac{\sqrt{30}i}{20}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}i}{20} x=\frac{\sqrt{30}i}{20}$$