# How do you solve 3-13s=3-8s+s^2?

Apr 11, 2016

$s = - 5$

#### Explanation:

Our aim is to isolate and find the value of $s$

color(blue)(3-13s=3-8s+s^2

Subtract $3$ both sides

$\rightarrow \textcolor{b l u e}{3} - 13 s - \textcolor{b l u e}{3} = \textcolor{b l u e}{3} - 8 s + {s}^{2} - \textcolor{b l u e}{3}$

$\rightarrow - 13 s = - 8 s + {s}^{2}$

Add $8 s$ both sides

$\rightarrow \textcolor{b l u e}{- 13 s} + \textcolor{b l u e}{8 s} = \textcolor{b l u e}{- 8 s} + {s}^{2} + \textcolor{b l u e}{- 8}$

$\rightarrow - 5 s = {s}^{2}$

From now use logic!

We know that color(brown)(s^2=s*s

So,

$\rightarrow - 5 s = s \cdot s$

Divide both sides by $s$

$\rightarrow \frac{- 5 \cancel{\textcolor{b l u e}{s}}}{\cancel{\textcolor{b l u e}{s}}} = \frac{s \cdot \cancel{\textcolor{b l u e}{s}}}{\cancel{\textcolor{b l u e}{s}}}$

color(green)(rArr-5=s