SOLUTION: 2. Solve {{{x+3*sqrt(x)-40=0}}}

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Question 143724: 2. Solve x%2B3%2Asqrt%28x%29-40=0



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B3%2Asqrt%28x%29-40=0 Start with the given equation


Let y=sqrt%28x%29. So y%5E2=%28sqrt%28x%29%29%5E2=x. In other words, y%5E2=x


y%5E2%2B3y-40=0 Replace sqrt%28x%29 with y and replace x with y%5E2



%28y%2B8%29%28y-5%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
y%2B8=0 or y-5=0

y=-8 or y=5 Now solve for y in each case


So the y values are

y=-8 or y=5




Remember, we let y=sqrt%28x%29.


-8=sqrt%28x%29 Plug in y=-8


%28-8%29%5E2=x Square both sides


64=x Square -8 to get 64


So the first possible answer is x=64. But we need to check our answer


Check:

x%2B3%2Asqrt%28x%29-40=0 Start with the given equation


64%2B3%2Asqrt%2864%29-40=0 Plug in x=64


64%2B3%2A8-40=0 Take the square root of 64 to get 8


64%2B24-40=0 Multiply


48=0 Combine like terms. Since this is not true, this means that x=64 is not a solution



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5=sqrt%28x%29 Now plug in y=5 (this is the other y-value we found previously)


%285%29%5E2=x Square both sides


25=x Square 5 to get 25


So the second possible answer is x=25. But we need to check our answer



Check:

x%2B3%2Asqrt%28x%29-40=0 Start with the given equation


25%2B3%2Asqrt%2825%29-40=0 Plug in x=25


25%2B3%2A5-40=0 Take the square root of 25 to get 5


25%2B15-40=0 Multiply


0=0 Combine like terms. Since this is true, this means that x=25 is a solution



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Answer:



So the solution is x=25