Solve i(1-q)/1-qquad1/27*x^2=3

$$\frac { i ( 1 - q ) } { 1 - q } \quad \frac { 1 } { 27 } \cdot x ^ { 2 } = 3$$

Solve for q

$$q\neq 1$$

$$x=\sqrt{2}\left(-\frac{9}{2}+\frac{9}{2}i\right)\text{ or }x=\sqrt{2}\left(\frac{9}{2}-\frac{9}{2}i\right)$$

Steps for Solving Linear Equation

Variable q cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 27\left(q-1\right), the least common multiple of 1-q,27.

$$-27i\left(1-q\right)\times \frac{1}{27}x^{2}=81\left(q-1\right)$$

Multiply -27i and \frac{1}{27} to get -i.

$$-i\left(1-q\right)x^{2}=81\left(q-1\right)$$

Use the distributive property to multiply -i by 1-q.

$$\left(-i+iq\right)x^{2}=81\left(q-1\right)$$

Use the distributive property to multiply -i+iq by x^{2}.

$$-ix^{2}+iqx^{2}=81\left(q-1\right)$$

Use the distributive property to multiply 81 by q-1.

$$-ix^{2}+iqx^{2}=81q-81$$

Subtract 81q from both sides.

$$-ix^{2}+iqx^{2}-81q=-81$$

Subtract -ix^{2} from both sides.

$$iqx^{2}-81q=-81-\left(-ix^{2}\right)$$

Multiply -1 and -i to get i.

$$iqx^{2}-81q=-81+ix^{2}$$

Combine all terms containing q.

$$\left(ix^{2}-81\right)q=-81+ix^{2}$$

The equation is in standard form.

$$\left(ix^{2}-81\right)q=ix^{2}-81$$

Divide both sides by ix^{2}-81.

$$\frac{\left(ix^{2}-81\right)q}{ix^{2}-81}=\frac{ix^{2}-81}{ix^{2}-81}$$

Dividing by ix^{2}-81 undoes the multiplication by ix^{2}-81.

$$q=\frac{ix^{2}-81}{ix^{2}-81}$$

Divide ix^{2}-81 by ix^{2}-81.

$$q=1$$

Variable q cannot be equal to 1.

$$q\in \emptyset$$

Solve for x

$$x=\sqrt{2}\left(-\frac{9}{2}+\frac{9}{2}i\right)$$

$$x=\sqrt{2}\left(\frac{9}{2}-\frac{9}{2}i\right)\text{, }q\neq 1$$