Question 174691
{{{8/x+108/x^2=96.88}}} Start with the given equation.



{{{x^2(8/cross(x))+x^2(108/cross(x^2))=96.88x^2}}} Multiply EVERY term by the LCD {{{x^2}}} to clear out the fractions.



{{{8x+108=96.88x^2}}} Simplify



{{{800x+10800=9688x^2}}} Multiply both sides by 100 to make every number a whole number.



{{{-9688x^2+800x+10800=0}}} Subtract {{{9688x^2}}} from both sides.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=-9688}}}, {{{b=800}}}, and {{{c=10800}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(800) +- sqrt( (800)^2-4(-9688)(10800) ))/(2(-9688))}}} Plug in  {{{a=-9688}}}, {{{b=800}}}, and {{{c=10800}}}



{{{x = (-800 +- sqrt( 640000-4(-9688)(10800) ))/(2(-9688))}}} Square {{{800}}} to get {{{640000}}}. 



{{{x = (-800 +- sqrt( 640000--418521600 ))/(2(-9688))}}} Multiply {{{4(-9688)(10800)}}} to get {{{-418521600}}}



{{{x = (-800 +- sqrt( 640000+418521600 ))/(2(-9688))}}} Rewrite {{{sqrt(640000--418521600)}}} as {{{sqrt(640000+418521600)}}}



{{{x = (-800 +- sqrt( 419161600 ))/(2(-9688))}}} Add {{{640000}}} to {{{418521600}}} to get {{{419161600}}}



{{{x = (-800 +- sqrt( 419161600 ))/(-19376)}}} Multiply {{{2}}} and {{{-9688}}} to get {{{-19376}}}. 



{{{x = (-800 +- 80*sqrt(65494))/(-19376)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-800+80*sqrt(65494))/(-19376)}}} or {{{x = (-800-80*sqrt(65494))/(-19376)}}} Break up the expression.  



So the answers are {{{x = (-800+80*sqrt(65494))/(-19376)}}} or {{{x = (-800-80*sqrt(65494))/(-19376)}}} 



which approximate to {{{x=-1.015}}} or {{{x=1.098}}}