Solve -1/2x*1/2x=19/90

$$- \frac { 1 } { 2 } x \cdot \frac { 1 } { 2 } x = \frac { 19 } { 90 }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{190}i}{15}\approx -0-0.918936583i$$

$$x=\frac{\sqrt{190}i}{15}\approx 0.918936583i$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$-\frac{1}{2}x^{2}\times \frac{1}{2}=\frac{19}{90}$$

Multiply -\frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{2\times 2}x^{2}=\frac{19}{90}$$

Do the multiplications in the fraction \frac{-1}{2\times 2}.

$$\frac{-1}{4}x^{2}=\frac{19}{90}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{1}{4}x^{2}=\frac{19}{90}$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x^{2}=\frac{19}{90}\left(-4\right)$$

Express \frac{19}{90}\left(-4\right) as a single fraction.

$$x^{2}=\frac{19\left(-4\right)}{90}$$

Multiply 19 and -4 to get -76.

$$x^{2}=\frac{-76}{90}$$

Reduce the fraction \frac{-76}{90} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{38}{45}$$

The equation is now solved.

$$x=\frac{\sqrt{190}i}{15} x=-\frac{\sqrt{190}i}{15}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$-\frac{1}{2}x^{2}\times \frac{1}{2}=\frac{19}{90}$$

Multiply -\frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{2\times 2}x^{2}=\frac{19}{90}$$

Do the multiplications in the fraction \frac{-1}{2\times 2}.

$$\frac{-1}{4}x^{2}=\frac{19}{90}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{1}{4}x^{2}=\frac{19}{90}$$

Subtract \frac{19}{90} from both sides.

$$-\frac{1}{4}x^{2}-\frac{19}{90}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{4} for a, 0 for b, and -\frac{19}{90} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{4}\right)\left(-\frac{19}{90}\right)}}{2\left(-\frac{1}{4}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{4}\right)\left(-\frac{19}{90}\right)}}{2\left(-\frac{1}{4}\right)}$$

Multiply -4 times -\frac{1}{4}.

$$x=\frac{0±\sqrt{-\frac{19}{90}}}{2\left(-\frac{1}{4}\right)}$$

Take the square root of -\frac{19}{90}.

$$x=\frac{0±\frac{\sqrt{190}i}{30}}{2\left(-\frac{1}{4}\right)}$$

Multiply 2 times -\frac{1}{4}.

$$x=\frac{0±\frac{\sqrt{190}i}{30}}{-\frac{1}{2}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{190}i}{30}}{-\frac{1}{2}} when ± is plus.

$$x=-\frac{\sqrt{190}i}{15}$$

Now solve the equation x=\frac{0±\frac{\sqrt{190}i}{30}}{-\frac{1}{2}} when ± is minus.

$$x=\frac{\sqrt{190}i}{15}$$

The equation is now solved.

$$x=-\frac{\sqrt{190}i}{15} x=\frac{\sqrt{190}i}{15}$$