[tex]\bf x= \begin{cases} -7\\ -2 \end{cases}\implies \begin{cases} x=-7\implies &x+7=0\\ x=-2\implies &x+2=0 \end{cases}\implies (x+7)(x+2)=\stackrel{y}{0} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\mathbb{FOIL}}{x^2+9x+14=y}~\hfill[/tex]
For this case we have that a quadratic equation is of the form:
[tex]ax ^ 2 + bx + c = 0[/tex]
If you tell us that the solutions are given by:
[tex]x_{1}=-7\\x_ {2}=-2[/tex]
So, we have:
[tex](x + 7)(x + 2) = 0[/tex]
We apply distributive property:
[tex]x ^ 2 + 2x + 7x + 14 = 0[/tex]
We add similar terms:
[tex]x ^ 2 + 9x + 14 =0[/tex]
Answer:
[tex]x^2+9x+14=0[/tex]
[tex]a=1\\b=9\\c=14[/tex]
