Question 189277
The additive inverse of a number divided by 16 is the same as 1 less than -5 times its reciprocal.
 Find the number.
:
Let x = "a number"
{{{(-x)/16}}} = -5({{{1/x}}}) - 1 
{{{(-x)/16}}} = {{{-5/x}}} - 1
multiply equation by -1, get rid of all these negatives:
{{{x/16}}} = {{{5/x}}} + 1
Multiply equation by 16x, results:
x^2 = 16(5) + 16x
:
x^2 = 80 + 16x
:
x^2 -16x - 80 = 0
Factors to:
(x-20)(x+4) = 0
:
x = +20
x = -4
:
:
Check solutions in original equation:
x=20
{{{(-20)/16}}} = -5({{{1/20}}}) - 1 
-1.25 = -.25 - 1
and
x=-4
{{{(-(-4))/16}}} = -5({{{1/(-4)}}}) - 1 
+.25 = +1.25 - 1