5. divide and simplify if possible. √250x16√2x 6. what is the solution of the equation? √2x+13−5=x

5.  (5x^7)√(5x)

6.  x = -2

Step-by-step explanation:

5.

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6.

There is always the possibility of extraneous solutions for equations like this. We can check.

  √(2·(-6)+13) -5 = -6 . . . . substitute -6 for x

  √1 -5 = -6 . . . . . . . . . . . . not true; -6 is an extraneous solution

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  √2·(-2)+13) -5 = -2

  √9 -5 = -2 . . . . . . . . . . . true; x = -2 is the solution

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The attached graph has the equation rewritten so it is of the form

  f(x) = 0

where

  f(x) = √(2x+13) -5 -x

The x-intercept is highlighted on the graph. It is x=-2. You can see that if the negative branch of the square root function were included, it might make an x-intercept at x=-6. For our purposes, the square root function is the positive square root only, so that branch is not included and -6 is an extraneous solution.

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step-by-step explanation: