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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
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