Solve 1/2a_{1}q^2=-4

$$\frac { 1 } { 2 } a _ { 1 } q ^ { 2 } = - 4$$

Solve for a_1

$$a_{1}=-\frac{8}{q^{2}}$$

$$q\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{q^{2}}{2}a_{1}=-4$$

Divide both sides by \frac{1}{2}q^{2}.

$$\frac{2\times \frac{q^{2}}{2}a_{1}}{q^{2}}=\frac{-4\times 2}{q^{2}}$$

Dividing by \frac{1}{2}q^{2} undoes the multiplication by \frac{1}{2}q^{2}.

$$a_{1}=\frac{-4\times 2}{q^{2}}$$

Divide -4 by \frac{1}{2}q^{2}.

$$a_{1}=-\frac{8}{q^{2}}$$

Solve for q (complex solution)

$$q=-2\sqrt{2}ia_{1}^{-\frac{1}{2}}$$

$$q=2\sqrt{2}ia_{1}^{-\frac{1}{2}}\text{, }a_{1}\neq 0$$

Solve for q

$$q=2\sqrt{-\frac{2}{a_{1}}}$$

$$q=-2\sqrt{-\frac{2}{a_{1}}}\text{, }a_{1}<0$$