Solution: the second option x = - 4.
Explanation:
1) given √(3x + 28) - 8 = x
2) transpose -8 to the right side
√(3x + 28) = x + 8
3) square both sides
3x + 28 = (x + 8)²
3x + 28 = x² + 16x + 64
4) transpose all the terms to the right side
x² + 16x + 64 - 3x - 28 = 0
x² + 13x + 36 = 0
5) factor
(x + 9) (x + 4) = 0
6) equal each factor to 0
x = - 9
x = - 4
7) Replace in the equation to discard extraneous solutions
a) x = - 9
√ (3(-9) + 28) - 8 = - 9
√ (-27 + 28) - 8 = - 9
this is a extraneous solution because the amount inside the root is negative.
b) x = - 4
√ (3(-4) + 28) - 8 = - 4
√ ( -12 + 28) - 8 = - 4
√ (16) - 8 = - 4
4 - 8 = - 4
-4 = - 4
This is the solution.
