x2 + 6x + 5 = (x + 1)(x + 5)
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(x + 1)(x + 5)
(x + 1)(x + 5)
32
Suppose the number is x. Then x + 5/x = 6 Multiplying throughout by x, x2+5 = 6x or x2 - 6x + 5 = 0 which can be factorised into (x-1)*(x-5)=0 So x = 1 (and 5 times its reciprocal is 5) or x = 5 (and 5 times its reciprocal is 1).
6x - 5 -5 = 0 6x -10 = 0 +10=+10 6x=10 x= about 1.4