Solve 4/8-x^2=2

$$\frac { 4 } { 8 } - x ^ { 2 } = 2$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{2}\approx -0-1.224744871i$$

$$x=\frac{\sqrt{6}i}{2}\approx 1.224744871i$$

Steps by Finding Square Root

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}-x^{2}=2$$

Subtract \frac{1}{2} from both sides.

$$-x^{2}=2-\frac{1}{2}$$

Subtract \frac{1}{2} from 2 to get \frac{3}{2}.

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

Divide both sides by -1.

$$x^{2}=\frac{\frac{3}{2}}{-1}$$

Express \frac{\frac{3}{2}}{-1} as a single fraction.

$$x^{2}=\frac{3}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

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

Fraction \frac{3}{-2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

The equation is now solved.

$$x=\frac{\sqrt{6}i}{2} x=-\frac{\sqrt{6}i}{2}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}-x^{2}=2$$

Subtract 2 from both sides.

$$\frac{1}{2}-x^{2}-2=0$$

Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.

$$-\frac{3}{2}-x^{2}=0$$

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.

$$-x^{2}-\frac{3}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -\frac{3}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{3}{2}\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{3}{2}\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-\frac{3}{2}\right)}}{2\left(-1\right)}$$

Multiply 4 times -\frac{3}{2}.

$$x=\frac{0±\sqrt{-6}}{2\left(-1\right)}$$

Take the square root of -6.

$$x=\frac{0±\sqrt{6}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\sqrt{6}i}{-2}$$

Now solve the equation x=\frac{0±\sqrt{6}i}{-2} when ± is plus.

$$x=-\frac{\sqrt{6}i}{2}$$

Now solve the equation x=\frac{0±\sqrt{6}i}{-2} when ± is minus.

$$x=\frac{\sqrt{6}i}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{6}i}{2} x=\frac{\sqrt{6}i}{2}$$