Solve 8x^2-1text{sas}=-1/2ix

$$8 x ^ { 2 } - 1 \text { sas } = - \frac { 1 } { 2 } i x$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x\left(16x+i\right)}{2s^{2}}\text{, }&s\neq 0\\a\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=-\frac{1}{16}i\right)\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$8x^{2}-s^{2}a=-\frac{1}{2}ix$$

Subtract 8x^{2} from both sides.

$$-s^{2}a=-\frac{1}{2}ix-8x^{2}$$

The equation is in standard form.

$$\left(-s^{2}\right)a=-8x^{2}-\frac{ix}{2}$$

Divide both sides by -s^{2}.

$$\frac{\left(-s^{2}\right)a}{-s^{2}}=-\frac{\frac{x\left(16x+i\right)}{2}}{-s^{2}}$$

Dividing by -s^{2} undoes the multiplication by -s^{2}.

$$a=-\frac{\frac{x\left(16x+i\right)}{2}}{-s^{2}}$$

Divide -\frac{x\left(i+16x\right)}{2} by -s^{2}.

$$a=\frac{x\left(16x+i\right)}{2s^{2}}$$

Solve for s

$$\left\{\begin{matrix}s=-\frac{ia^{-\frac{1}{2}}\sqrt{2x}\sqrt{-i-16x}}{2}\text{; }s=\frac{ia^{-\frac{1}{2}}\sqrt{2x}\sqrt{-i-16x}}{2}\text{, }&a\neq 0\\s\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=-\frac{1}{16}i\right)\text{ and }a=0\end{matrix}\right.$$