Solve 8x^2+55-2=0

$$8 { x }^{ 2 } +55-2=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{106}i}{4}\approx -0-2.573907535i$$

$$x=\frac{\sqrt{106}i}{4}\approx 2.573907535i$$

Steps by Finding Square Root

Subtract 2 from 55 to get 53.

$$8x^{2}+53=0$$

Subtract 53 from both sides. Anything subtracted from zero gives its negation.

$$8x^{2}=-53$$

Divide both sides by 8.

$$x^{2}=-\frac{53}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{106}i}{4} x=-\frac{\sqrt{106}i}{4}$$

Steps Using the Quadratic Formula

Subtract 2 from 55 to get 53.

$$8x^{2}+53=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 53 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\times 53}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\times 53}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\times 53}}{2\times 8}$$

Multiply -32 times 53.

$$x=\frac{0±\sqrt{-1696}}{2\times 8}$$

Take the square root of -1696.

$$x=\frac{0±4\sqrt{106}i}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±4\sqrt{106}i}{16}$$

Now solve the equation x=\frac{0±4\sqrt{106}i}{16} when ± is plus.

$$x=\frac{\sqrt{106}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{106}i}{16} when ± is minus.

$$x=-\frac{\sqrt{106}i}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{106}i}{4} x=-\frac{\sqrt{106}i}{4}$$