Solve -x=x^2-x+3/8

$$- x = x ^ { 2 } - x + \frac { 3 } { 8 }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{4}\approx -0-0.612372436i$$

$$x=\frac{\sqrt{6}i}{4}\approx 0.612372436i$$

Steps by Finding Square Root

Subtract x^{2} from both sides.

$$-x-x^{2}=-x+\frac{3}{8}$$

Add x to both sides.

$$-x-x^{2}+x=\frac{3}{8}$$

Combine -x and x to get 0.

$$-x^{2}=\frac{3}{8}$$

Divide both sides by -1.

$$x^{2}=\frac{\frac{3}{8}}{-1}$$

Express \frac{\frac{3}{8}}{-1} as a single fraction.

$$x^{2}=\frac{3}{8\left(-1\right)}$$

Multiply 8 and -1 to get -8.

$$x^{2}=\frac{3}{-8}$$

Fraction \frac{3}{-8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$x^{2}=-\frac{3}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{6}i}{4} x=-\frac{\sqrt{6}i}{4}$$

Steps Using the Quadratic Formula

Subtract x^{2} from both sides.

$$-x-x^{2}=-x+\frac{3}{8}$$

Add x to both sides.

$$-x-x^{2}+x=\frac{3}{8}$$

Subtract \frac{3}{8} from both sides.

$$-x-x^{2}+x-\frac{3}{8}=0$$

Combine -x and x to get 0.

$$-x^{2}-\frac{3}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -\frac{3}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{3}{8}\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{3}{8}\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-\frac{3}{8}\right)}}{2\left(-1\right)}$$

Multiply 4 times -\frac{3}{8}.

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

Take the square root of -\frac{3}{2}.

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

Multiply 2 times -1.

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

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

$$x=-\frac{\sqrt{6}i}{4}$$

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

$$x=\frac{\sqrt{6}i}{4}$$

The equation is now solved.

$$x=-\frac{\sqrt{6}i}{4} x=\frac{\sqrt{6}i}{4}$$