Given the equation:
[tex](x+7)(x-2)=(x+1)^2[/tex]
We will solve the equation as follows:
[tex]\begin{gathered} (x+7)(x-2)=(x+1)(x+1) \\ x(x-2)+7(x-2)=x(x+1)+1\cdot(x+1) \\ x^2-2x+7x-14=x^2+x+x+1 \\ x^2+5x-14=x^2+2x+1 \end{gathered}[/tex]
Combine the like terms:
[tex]\begin{gathered} x^2-x^2+5x-2x=14+1 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]
So, the answer will be option A:
The solution set is {5}
