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Let the number be m & n

Hence

mn = -8

m + n = 1

It follows that m = -8/n

Substitute

-8/n + n = 1

Multiply through by 'n'

-8 + n^2 = n

n^2 - n - 8 = 0

This does NOT factor so Complete the Square

n^2 - n = 8

(n - 1/2)^2 - (1/2)^2 = 8

(n - 1/2)^2 - 1/4 = 8

(n - 1/2(^2 = 8 1/4 = 33/4

Square Root both sides

n - 1/2 = +/-sqrt(33) / 2

n = 1/2 +/- sqrt(33) / 2

or

n = (1 +/- sqrt(33))/ 2

Q: What multiplies to -8 and adds to 7?

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