Answer: (-7 ; -3 )
Step-by-step explanation:
[tex]\rm \displaystyle 1-st \ \ method \\\\ \large \boldsymbol {} \rm 4x^2+40x+84 =0 \ \ |\div4 \\\\x^2+10x+21=0 \\\\ \begin{cases} \rm x_1+x_2=-10 \\ \rm x_1x_2=21 \end{cases} \to x_1=-7 \ \ ; \ \ x_2=-3 \\\\\\ Answer : (-7 \ \ ; \ \ -3 ) \\\\ ---------- \\\\2-nd \ \ method \\\\ 4x^2+40x+84=0 \ \ |\div 4 \\\\ x^2+10x+21=0 \\\\ x^2+\underbrace{7x+3x}_{{10x}}+21=0 \\\\ (x^2+3x)+(7x+21)=0 \\\\ x\underline {(x+3)}+7 \underline{(x+3)}=0 \\\\ (x+7)(x+3)=0 \to x_1=-7 \ \ ; \ \ x_2=-3 \\\\[/tex]
[tex]\large \boldsymbol {} \rm Answer : (-7 \ \ ; \ \ -3)[/tex]
