[tex]\begin{gathered} x^2+6x\text{ = - }5 \\ x^2+6x\text{ +5 = - }5+5\text{ We add 5 to each side} \\ x^2+6x+5=0\text{ We now have a quadratic equation} \\ \\ x=\frac{\text{ -b }\pm\text{ }\sqrt{b^2\text{ - }4ac}}{2a}\text{ We have to use the quadratic formula} \\ \\ x=\frac{\text{ -6 }\pm\sqrt{(\text{ 6\rparen}^2}\text{ - }4(1)(5)}{2(1)} \\ \\ x=\text{ }\frac{\text{ -6 }\pm\text{ }\sqrt{36\text{ -20}}}{2} \\ \\ x=\frac{\text{ -6 }\pm\text{ }\sqrt{16}}{2} \\ \\ x=\frac{\text{ -6 }\pm\text{ 4}}{2} \\ \\ x1=\frac{\text{ -6 + 4}}{2}=\frac{\text{ -2}}{2}=\text{ -1} \\ \\ x2=\frac{\text{ -6 - 4}}{2}=\text{ }\frac{\text{ -10}\frac{}{}}{2}=\text{ -}5 \end{gathered}[/tex]
So, the two possible solutions are -1 and -5
