# Quadratic Equations| Algebra| ENGG10 LE3| Problem 1

#### Solve this formula for s in terms of r.

SOLUTION:

Multiply both sides by the LCD $s\left(r-s\right)$

$r\left(r-s\right)=s\left(s\right)$

$r^2-rs=s^2$

$s^2+rs-r^2=0$

Since we are solving for s in terms of r, we treat r as a constant. Thus, this is quadratic in s with the following:  $a=1,\:b=r,\:c=-r^2$

Solve for s using the quadratic formula

$s=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$s=\frac{-r\pm \sqrt{r^2-4\left(1\right)\left(-r^2\right)}}{2\left(1\right)}$

$s=\frac{-r\pm \sqrt{r^2+4r^2}}{2}$

$s=\frac{-r\pm \:\sqrt{5r^2}}{2}$

$s=\frac{-r\pm r\sqrt{5}}{2}$

$s=\frac{r\left(-1\pm \sqrt{5}\right)}{2}$