Solve S=6000(1+r)^2

$$S = 6000 ( 1 + r ) ^ { 2 }$$

Solve for S

$$S=6000\left(r+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+r\right)^{2}.

$$S=6000\left(1+2r+r^{2}\right)$$

Use the distributive property to multiply 6000 by 1+2r+r^{2}.

$$S=6000+12000r+6000r^{2}$$

Solve for r

$$r=-\frac{\sqrt{15S}}{300}-1$$

$$r=\frac{\sqrt{15S}}{300}-1\text{, }S\geq 0$$