Answer
The number is either = -2 or -3
Work Step by Step
Let number be $\Longrightarrow$ x
Product of 6 and the numbers reciprocal = 6($\frac{1}{x}$) = $\frac{6}{x}$
Given,
x + $\frac{6}{x}$ = -5
Multiplying both sides by x,
x(x + $\frac{6}{x}$) = x(-5)
Thus x(x) + x($\frac{6}{x}$) = x(-5)
$x^{2}$ + 6 = -5x
$x^{2}$ + 5x + 6 = -5x + 5x
Thus
$x^{2}$ + 5x + 6 = 0
Thus, we need factors such that their product is 6 and sum is 5.
Thus the factors are 3 and 2.
Thus $x^{2}$ + 3x + 2x + 6 = 0
x(x + 3) + 2 (x + 3) = 0
(x + 2) (x + 3) = 0
Thus either x + 2 = 0, so x = -2
or x + 3 = 0, so x = -3
Thus x = -2 or x = -3
