Solve 614x^2+16=0

$$614 x ^ { 2 } + 16 = 0$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{614}i}{307}\approx -0-0.161426862i$$

$$x=\frac{2\sqrt{614}i}{307}\approx 0.161426862i$$

Steps by Finding Square Root

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$614x^{2}=-16$$

Divide both sides by 614.

$$x^{2}=\frac{-16}{614}$$

Reduce the fraction \frac{-16}{614} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{8}{307}$$

The equation is now solved.

$$x=\frac{2\sqrt{614}i}{307} x=-\frac{2\sqrt{614}i}{307}$$

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.

$$614x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 614 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 614\times 16}}{2\times 614}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 614\times 16}}{2\times 614}$$

Multiply -4 times 614.

$$x=\frac{0±\sqrt{-2456\times 16}}{2\times 614}$$

Multiply -2456 times 16.

$$x=\frac{0±\sqrt{-39296}}{2\times 614}$$

Take the square root of -39296.

$$x=\frac{0±8\sqrt{614}i}{2\times 614}$$

Multiply 2 times 614.

$$x=\frac{0±8\sqrt{614}i}{1228}$$

Now solve the equation x=\frac{0±8\sqrt{614}i}{1228} when ± is plus.

$$x=\frac{2\sqrt{614}i}{307}$$

Now solve the equation x=\frac{0±8\sqrt{614}i}{1228} when ± is minus.

$$x=-\frac{2\sqrt{614}i}{307}$$

The equation is now solved.

$$x=\frac{2\sqrt{614}i}{307} x=-\frac{2\sqrt{614}i}{307}$$