Solve the radical equation the square root of (x + 6) equal to x.

1. The radical is already alone on the left, so square both sides. 2. Squaring gives x plus 6 equal to x squared. 3. Rearranging gives x squared minus x minus 6 equal to 0. 4. Factoring gives the brackets (x minus 3) and (x plus 2). 5. So the proposed solutions are x equal to 3 and x equal to negative 2. 6. Test x equal to 3: the square root of 9 is 3, which matches the right side. 7. Test x equal to negative 2: the square root of 4 is 2, but the right side is negative 2, so it fails. 8. Squaring both sides created that second root, so it is extraneous and only x equal to 3 survives. 9. Keeping both values skips the check that squaring makes necessary. 10. Rejecting both values ignores that x equal to 3 does satisfy the original equation. _Source: OpenStax College Algebra (CC BY 4.0), section 2.6 Other Types of Equations_