SOLUTION: sqrt(5-x)=x-3

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Question 134950: sqrt(5-x)=x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285-x%29=x-3 Start with the given equation


5-x=%28x-3%29%5E2 Square both sides


5-x=x%5E2-6x%2B9 Foil the right side


0=x%5E2-6x%2B9-5%2Bx Subtract 5 from both sides. Add x to both sides.


0=x%5E2-5x%2B4 Combine like terms


0=%28x-4%29%28x-1%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-4=0 or x-1=0

x=4 or x=1 Now solve for x in each case


So our possible answers are

x=4 or x=1


However, if you plug in x=1, you'll notice that the equation is not equal. So this shows use that x=1 is not a solution



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Answer:

So our only solution is x=4