Question 27822
If 5 is added to a number (5+x), the result is the same as (equals) that obtained by multiplying its reciprocal (1/x) by 14 (times 14). What is the number?

{{{5+x=(1/x)*14}}}
{{{5+x=14/x}}}Multiply all terms by x:
{{{5x+x^2=14}}}Rearrange:
{{{x^2+5x=14}}}Solving by completing the square (adding (5/2)^2 to both sides):
{{{x^2+5x+(5/2)^2=14+(5/2)^2}}}
{{{(x+5/2)^2=81/4}}}
{{{x+5/2= 0 +-sqrt(81/4)}}}(Ignore the 0, just makes the equation editor work)
{{{x+5/2= 0 +- 9/2}}} (Again, ignore the 0)
{{{x=-5/2+- 9/2}}}
{{{x=(-5+- 9)/2}}}
So x = {{{(-5+9)/2}}}=2 or {{{(-5-9)/2}}}=-7

If 5 is added to 2, the result (7) is the same as its reciprocal (1/2) multiplied by 14 (1/2*14=7) Check.
If 5 is added to -7 the result (-2) is the same as its reciprocal (-1/7) multiplied by 14 (-1/7*14=-2) Check.