We have x² - |x| - 30 = 0
If x ≥ 0, then we have x² – x – 30 = 0 ⇒ (x – 6) (x + 5) = 0 ⇒ x = 6, - 5. But since x ≥ 0, hence x = 6. Therefore (x + 5) is incorrect.
If x < 0, then x² + x – 30 = 0 ⇒ (x + 6) (x – 5) = 0 ⇒ x = - 6, 5. But since x < 0 ⇒ x = -6.
Hence (x – 5) is incorrect. Also x + 7 cannot be the factor of the above equation, so it is also not possible.