Solve 11x^2+2=0

$$11 x ^ { 2 } + 2 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{22}i}{11}\approx -0-0.426401433i$$

$$x=\frac{\sqrt{22}i}{11}\approx 0.426401433i$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$11x^{2}=-2$$

Divide both sides by 11.

$$x^{2}=-\frac{2}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{22}i}{11} x=-\frac{\sqrt{22}i}{11}$$

Steps Using the Quadratic Formula

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.

$$11x^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\times 2}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\times 2}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\times 2}}{2\times 11}$$

Multiply -44 times 2.

$$x=\frac{0±\sqrt{-88}}{2\times 11}$$

Take the square root of -88.

$$x=\frac{0±2\sqrt{22}i}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±2\sqrt{22}i}{22}$$

Now solve the equation x=\frac{0±2\sqrt{22}i}{22} when ± is plus.

$$x=\frac{\sqrt{22}i}{11}$$

Now solve the equation x=\frac{0±2\sqrt{22}i}{22} when ± is minus.

$$x=-\frac{\sqrt{22}i}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{22}i}{11} x=-\frac{\sqrt{22}i}{11}$$