If the two numbers are x & y, then x*y = 210, and x + y = -23.
From the 2nd equation, let y = -23 - x, then substitute into first: x*(-23 - x) = 210, then expand:
-23*x - x² = 210, rearrange: x² + 23*x + 210 = 0, using the quadratic formula, we can see that the solution is complex : square root of [23² - 4*210] = sqrt(-311).
So there are no two real numbers which satisfy the conditions.
The factor pairs of 210 are (210,1)(105,2)(70,3)(42,5)(35,6)(30,7)(21,10)(15,14) None of them add up to 23. If that was -210, you could use 30 and -7.
83
-337
-397
There aren't any whole numbers that satisfy these conditions. The only numbers that multiply to 23 are 23 and 1.
23
73
37
53
There are no two real numbers that do, but two complex numbers do: (3.5 + i 3.5 √23) and (3.5 - i 3.5 √23) If you want them to add to 7 and multiply to -294, then the two real numbers -14 and 21 work. Or if you want them to add to -7 and multiply to -294, then the two real numbers 14 and -21 work. To add to -7 and multiply to 294, the following two complex numbers work: (-3.5 + i 3.5 √23) and (-3.5 - i 3.5 √23)
-15+-8=-23 -15*-8=120
-27