Question 119128

{{{x/2-18/x+5/2=0}}} Start with the given equation




{{{(2x)(x/2-18/x+5/2)=(2x)(0)}}} Multiply both sides by the LCM of 2x. This will eliminate the fractions 



{{{x^2-36+5x=0}}} Distribute and multiply the LCM to each side




{{{x^2+5x-36=0}}} Rearrange the terms




{{{(x+9)(x-4)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+9=0}}} or  {{{x-4=0}}} 


{{{x=-9}}} or  {{{x=4}}}    Now solve for x in each case



So our answer is 

 {{{x=-9}}} or  {{{x=4}}} 



Notice if we graph {{{y=x^2+5x-36}}} we can see that the roots are {{{x=-9}}} and  {{{x=4}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2+5x-36) }}}