Question

What’s the answer ???

Answer 1

You can divide the whole equation by 2 to get

$x^2 -\frac{1}{2}x-5=0$

This is useful, in this case, because any quadratic equation with leading coefficient 1 can be read as

$x^2-sx+p = 0$

where s is the sum of the two solutions, and p is their product.

So, we know that the two solutions sum to 1/2, and give -5 when multiplied.

But we already know that one solution is 5/2, so if we call the other solution x we have

$\frac{5}[2}+x = \frac{1}{2} \iff x = \frac{1}{2} - \frac{5}[2} = \frac{-4}{2} = -2$

Just to check, let's see that they give -5 when multiplied:

$\frac{5}[2} \cdot (-2) = -5$

So it works! The other solution is -2.