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|x|=x^2+7x

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1 Answer

|x|=x^2+7x

0 is one solution

  0^2 + 7x0 = 0 = |0|

Assume x is positive. 

Then |x| = x 

So then x =  x^2 +7x

            x^2 + 6x = 0

           x(x+6) = 0,

           possible solutions:  x= 0, x = -6

           x = -6 is not a solution.  Remember we assumed x was positive.

Assume x is negative.

    |x| = -x

     -x = x^2 +7x

     0 = x^2 + 8x

     0 = x(x-+8) 

     - 8 is a solution

     |-8| = 8 = (-8)^2 + 7X(-8)

                  = 64 - 56

                 = 8

Therefore 0 and -8 are solutions