## Algebra: A Combined Approach (4th Edition)

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