What two numbers when multiplied gives $-25$ and when added, $-10$? Factors of $25$ are; $1, 5, 25$
$$5 \times 5 = 25$$
$$5 + 5 = 10$$
$$-5 \times 5 = -25$$
$$-5 + 5 = 0$$
How can I solve this?
Thanks

Well one cannot solve this if only integers may be used. 
The answer is:
$$(a,b) = (5(\sqrt{2} - 1), -5(1+\sqrt{2}))$$
We can see this as we have
$$a*b = -25,\qquad a+b =-10.$$
From this it follows that $a = -10-b$, thus
$$-10b -b^2 = -25, \Rightarrow b^2+10b-25 = 0.$$
This can be solved quite easily, as this gives
$$b = \frac{-10\pm \sqrt{10^2-4*-25}}{2} = -5 \pm 5\sqrt{2}.$$
