What is the solution of |x - 4| = x^2 - 16

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The equation `|x - 4| = x^2 - 16` has to be solved.

`|x| = x` if `x >= 0` and `|x| = -x` if x < 0

This gives two equations from |x - 4| = x^2 - 16

- For `x - 4 >= 0` or `x >= 4`

x - 4 = x^2 - 16

=> x - 4 = (x - 4)(x + 4)

=> x + 4 = 1

=> x = -3

This is not possible as `x >= 4`

- For x - 4 < 0 or x < 4

-(x - 4) = x^2 - 16

=> 4 - x = (x - 4)(x + 4)

=> 1 = -(x + 4)

=> 1 = -x - 4

=> x = -5

This is less than 4

**The equation |x - 4| = x^2 - 16 has the solution x = -5**

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