[tex]\begin{gathered} \text{Given} \\ x^2+6x+8=0 \end{gathered}[/tex]
Determine the third term so that it is the perfect square of the trinomial.
Divide the coefficient of the second term, and square it. We get the following:
[tex]\begin{gathered} 6x\Rightarrow6 \\ \\ \Big(\frac{6}{2}\Big)^2 \\ =(3)^2 \\ =9 \end{gathered}[/tex]
This means that the third term should be 9. Since we already have 8 as the third term of the given equation, add 1 on both sides to get the perfect square on the left side. Therefore, we have the following steps.
[tex]\begin{gathered} x^2+6x+8=0 \\ x^2+6x+8+1=0+1 \\ x^2+6x+9=1 \\ (x+3)^2=1 \end{gathered}[/tex]
