Question

Como eu resolvo?
Passo a passo por favor.
(x+5).(x+1)=12

Answer 1

$(x+5).(x+1)=12\\ x*x+x*1+5*x+5*1=12\\ x^{2} +x+5x+5=12\\ x^{2} +6x+5=12\\ x^{2} +6x+5-12=0\\ x^{2} +6x-7=0$

$\begin{cases}a=1\\ b=6\\ c=-7\end{cases}$

$\boxed{\Delta=b ^{2}-4ac}\\\\ \Delta=6 ^{2}-4*1*(-7)\\ \Delta=36+28\\ \Delta=64$

$\boxed{x= \frac{-b\pm \sqrt{\Delta} }{2a}}\\\\\\ x= \frac{-6\pm \sqrt{64} }{2*1}\to~x= \frac{-6\pm8}{2}\to\begin{cases}x'= \frac{-6+8}{2}~\to~x'= \frac{2}{2}~\to~x'=1\\\\ x''= \frac{-6-8}{2}~\to~x''= \frac{-14}{2}~\to~x''=-7\end{cases}\\\\\\\\ \boxed{S=\{-7,1\}}$


Espero ter ajudado e tenha ótimos estudos =)