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

Question 143724: 2. Solve

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Let . So . In other words,

Replace with y and replace x with

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for y in each case

So the y values are

or

Remember, we let .

Plug in

Square both sides

Square -8 to get 64

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

Check:

Start with the given equation

Plug in

Take the square root of 64 to get 8

Multiply

Combine like terms. Since this is not true, this means that is not a solution

--------------------------------------------

Now plug in (this is the other y-value we found previously)

Square both sides

Square 5 to get 25

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

Check:

Start with the given equation

Plug in

Take the square root of 25 to get 5

Multiply

Combine like terms. Since this is true, this means that is a solution

--------------------------------------------

Answer:

So the solution is
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