Solve a(1-r)(1+r)=5

$$a ( 1 - r ) ( 1 + r ) = 5$$

Solve for a (complex solution)

$$a=\frac{5}{1-r^{2}}$$

$$r\neq 1\text{ and }r\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-r.

$$\left(a-ar\right)\left(1+r\right)=5$$

Use the distributive property to multiply a-ar by 1+r and combine like terms.

$$a-ar^{2}=5$$

Combine all terms containing a.

$$\left(1-r^{2}\right)a=5$$

Divide both sides by -r^{2}+1.

$$\frac{\left(1-r^{2}\right)a}{1-r^{2}}=\frac{5}{1-r^{2}}$$

Dividing by -r^{2}+1 undoes the multiplication by -r^{2}+1.

$$a=\frac{5}{1-r^{2}}$$

Solve for a

$$a=\frac{5}{1-r^{2}}$$

$$|r|\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-r.

$$\left(a-ar\right)\left(1+r\right)=5$$

Use the distributive property to multiply a-ar by 1+r and combine like terms.

$$a-ar^{2}=5$$

Combine all terms containing a.

$$\left(1-r^{2}\right)a=5$$

Divide both sides by -r^{2}+1.

$$\frac{\left(1-r^{2}\right)a}{1-r^{2}}=\frac{5}{1-r^{2}}$$

Dividing by -r^{2}+1 undoes the multiplication by -r^{2}+1.

$$a=\frac{5}{1-r^{2}}$$

Solve for r (complex solution)

$$r=-a^{-\frac{1}{2}}\sqrt{a-5}$$

$$r=a^{-\frac{1}{2}}\sqrt{a-5}\text{, }a\neq 0$$

Solve for r

$$r=\sqrt{\frac{a-5}{a}}$$

$$r=-\sqrt{\frac{a-5}{a}}\text{, }a\geq 5\text{ or }a<0$$