Question

Solve each of the following quadratic equations:

$x^2+6x+5=0$

Answer 1

We write, $6x=x+5x$ as $x^2\times 5=5x^2=x\times 5x$

$$\begin{gathered} \therefore x^2+6x+5=0 \\ \Rightarrow x^2+x+5x+5=0 \\ \Rightarrow x\left(x+1\right)+5\left(x+1\right)=0 \\ \Rightarrow \left(x+1\right)\left(x+5\right)=0 \end{gathered}$$

$$\begin{gathered} \Rightarrow x+1=0\mathrm{or}x+5=0 \\ \Rightarrow x=-1\mathrm{or}x=-5 \end{gathered}$$

Hence, the roots of the given equation are −1 and −5.