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
There aren't any whole numbers that satisfy these conditions. The only numbers that multiply to 23 are 23 and 1.
-337
-397
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