To factor the equation
[tex]x^2-9x+14=0[/tex]We will look for 2 numbers their product is 14, and their sum is 9
Since 14 = 2 x 7
Since 2 + 7 = 9
Then the factors will be (x - 2) and (x - 7)
[tex]\begin{gathered} x^2-9x+14=0 \\ (x-2)(x-7)=0 \end{gathered}[/tex]Equate each factor by 0 to find the values of x
[tex]x-2=0[/tex]Add 2 to both sides
[tex]\begin{gathered} x-2+2=0+2 \\ x=2 \end{gathered}[/tex][tex]x-7=0[/tex]Add 7 to both sides
[tex]\begin{gathered} x-7+7=0+7 \\ x=7 \end{gathered}[/tex]The values of x are 2 and 7
