Respuesta :

Edufirst
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.

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