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Let the numbers be 'm' & 'n'

Hence

mn = 51 (Multiplication)

m + n = -16 (Addition)

Algebraically rearrange

m = -16 -n

Ssubstitute

(-16-n) n = 51

-16n - n^2 = 51

n^(2) + 16n + 51 = 0 ( It is now in Quadratic form to solve).

Complete the Square

(n + 8)^2 - 8^(2) = -51

(n + 8)^2 = -51 + 64 = 13

Square root both sides

n + 8 = +/-sqrt(13)

n + 8 = +/- 3.60555....

n = -13.60555.... & -4.39444.... Are the two number.

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lenpollock

Lvl 16
7mo ago

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More answers

The factor pairs of 51 are (51,1)(17,3)

Even if you count their negative counterparts, none of them will add up to -16.

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Wiki User

10y ago
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Q: What 2 numbers multiply to 51 but add to -16?
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