Respuesta :
For x²-8x+12=0, we have:
[tex]x^2-8x+12=0[/tex]Factoring the expression:
[tex]\begin{gathered} \left(x^2-2x\right)+\left(-6x+12\right)=0 \\ x(x-2)-6(x-2)=0 \end{gathered}[/tex]Factor the common term x - 2:
[tex](x-2)(x-6)=0[/tex]Separate the solutions:
[tex]\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \\ and \\ x-6=0 \\ x-6+6=0+6 \\ x=6 \end{gathered}[/tex]Answer: x = 2 and x = 6
For x²-6x-7=0, we have:
[tex]x^2-6x-7=0[/tex]Factor the expression:
[tex]\begin{gathered} \left(x^2+x\right)+\left(-7x-7\right)=0 \\ x(x+1)-7(x+1)=0 \end{gathered}[/tex]Factor x + 1:
[tex](x+1)(x-7)=0[/tex]The solutions are:
[tex]\begin{gathered} x+1=0 \\ x+1-1=0-1 \\ x=-1 \\ and \\ x-7=0 \\ x-7+7=0+7 \\ x=7 \end{gathered}[/tex]Answer: x = -1 and x = 7
