Solve the equation. (enter your answers as a comma-separated list. round your answers to four decimal places.) x2e5x + 3xe5x − e5x = 0 x =

It's essential that you use " ^ " to indicate exponentiation if you want to communicate your ideas here accurately.

x2e5x + 3xe5x − e5x = 0 should be written as

x^2e^(5x) + 3xe^(5x) - 1e^(5x) = 0.

e^(5x) can be factored out of all four terms, leaving us with

e^(5x) [x^2 + 3x - 1] = 0.  e^(5x) is never zero, so no solution there.

However, we can set x^2 + 3x - 1 equal to zero and solve for x:

         -3 plus or minus sqrt(3^2 - 4(1)(-1) )
x =
                                 2
        -3 plus or minus sqrt(13)
   =
                                2

So the original equation has two roots.

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