SOLUTION: x/2-18/x+5/2=0

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Question 119128: x/2-18/x+5/2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%2F2-18%2Fx%2B5%2F2=0 Start with the given equation



%282x%29%28x%2F2-18%2Fx%2B5%2F2%29=%282x%29%280%29 Multiply both sides by the LCM of 2x. This will eliminate the fractions


x%5E2-36%2B5x=0 Distribute and multiply the LCM to each side



x%5E2%2B5x-36=0 Rearrange the terms



%28x%2B9%29%28x-4%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B9=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%5E2%2B5x-36 we can see that the roots are x=-9 and x=4 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2%2B5x-36%29+