Recall that the quadratic formula states that the solutions to the equation:
[tex]ax^2+bx+c=0[/tex]are:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]Therefore the solutions to the given equation are:
[tex]c=\frac{-40\pm\sqrt{40^2-4(25)(16)}}{2(25)}.[/tex]Simplifying the above result we get:
[tex]c=\frac{-40\pm\sqrt{1600-1600}}{2(25)}=\frac{-40}{50}=-\frac{4}{5}[/tex]Answer: The given equation has only one solution:
[tex]-\frac{4}{5}.[/tex]