Question

what numbers add to 2 and multiply to -56

Answer 1

The numbers are irrational, so they can't be exactly written down
using only digits.

In exact form, they are

     1 + √57
and
     1 - √57 .

In rounded form, they are

     8.54983
and
    -6.54983 .

Answer 2

-x² + 2x - 56 = 0

Use the quadratic formula to get the roots:

$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where the equation is ax² + bx + c =0

$\frac{-b \pm \sqrt{ b^2 -4( a)(c)} }{2(a)}\\\\ \frac{-2\pm \sqrt{2^2 -4(-1)(56)} }{2(-1)}\\ \\\frac{-2\pm \sqrt{228 } }{-2} = \frac{-2\pm \sqrt{4\times57 } }{-2} \\\\ = \frac{-2\pm 2\sqrt{57 } }{-2} \\\\ = \frac{-1\pm 1\sqrt{57 } }{-1} \\\\ =\boxed{\bf{ 1\pm \sqrt{57 } }}\\a$

The two numbers that add up to 2 and multiply to -56 are 1 + √57 and 1 - √57.