Solve 212x^2+5=0

$$212 x ^ { 2 } + 5 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{265}i}{106}\approx -0-0.153573779i$$

$$x=\frac{\sqrt{265}i}{106}\approx 0.153573779i$$

Steps by Finding Square Root

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$212x^{2}=-5$$

Divide both sides by 212.

$$x^{2}=-\frac{5}{212}$$

The equation is now solved.

$$x=\frac{\sqrt{265}i}{106} x=-\frac{\sqrt{265}i}{106}$$

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.

$$212x^{2}+5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 212 for a, 0 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 212\times 5}}{2\times 212}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 212\times 5}}{2\times 212}$$

Multiply -4 times 212.

$$x=\frac{0±\sqrt{-848\times 5}}{2\times 212}$$

Multiply -848 times 5.

$$x=\frac{0±\sqrt{-4240}}{2\times 212}$$

Take the square root of -4240.

$$x=\frac{0±4\sqrt{265}i}{2\times 212}$$

Multiply 2 times 212.

$$x=\frac{0±4\sqrt{265}i}{424}$$

Now solve the equation x=\frac{0±4\sqrt{265}i}{424} when ± is plus.

$$x=\frac{\sqrt{265}i}{106}$$

Now solve the equation x=\frac{0±4\sqrt{265}i}{424} when ± is minus.

$$x=-\frac{\sqrt{265}i}{106}$$

The equation is now solved.

$$x=\frac{\sqrt{265}i}{106} x=-\frac{\sqrt{265}i}{106}$$