|x|=x^2+7x

Question

solve the equation please

Answer 1

|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 

     

Answer 2

1. x = x² + 7x ---> x₁ = 0 , x₂ = -6
2. -x = x² + 7x ---> x₁ = 0 , x₂ = -8
x₁₂₃ = -8, -6, 0
l 0 l = 0     l -8 l = (-8)² + 7(-8)         l -6 l = (-6)² + 7(-6) 
  0 = 0         8   =  64 - 56                   6   =  36 - 42 
                   8   =      8                       6   ≠  -6  
Final answer  {-8, 0}