Question 913200
let x = unknown number



x = original number
1/x = reciprocal of original number


"The reciprocal of which number is the same as the original number, subtract one." translates to {{{1/x = x-1}}}


{{{1/x = x-1}}}


{{{1 = x*(x-1)}}}


{{{1 = x^2-x}}}


{{{0 = x^2-x-1}}}


{{{x^2-x-1=0}}}


Use the quadratic formula to solve for x


{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(-1)+-sqrt((-1)^2-4(1)(-1)))/(2(1))}}} Plug in {{{a = 1}}}, {{{b = -1}}}, {{{c = -1}}}  


{{{x = (1+-sqrt(1-(-4)))/(2)}}}


{{{x = (1+-sqrt(1+4))/(2)}}}


{{{x = (1+-sqrt(5))/2}}}


{{{x = (1+sqrt(5))/2}}} or {{{x = (1-sqrt(5))/2}}}


{{{x = 1.618034}}} or {{{x = -0.618034}}} Use a calculator to evaluate the expressions


So the number is either {{{x = 1.618034}}} or {{{x = -0.618034}}} 


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>
or you can visit my website here: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a>


Thanks,


Jim