Answer:
B
Step-by-step explanation:
[tex]\sqrt{x}[/tex] + 6 = x ( subtract 6 from both sides )
[tex]\sqrt{x}[/tex] = x - 6 ( square both sides )
x = (x - 6)² ← expand using FOIL
x = x² - 12x + 36 ( subtract x from both sides )
0 = x² - 13x + 36 , that is
x² - 13x + 36 = 0 ← in standard form
(x - 4)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 9 = 0 ⇒ x = 9
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 4
left side = [tex]\sqrt{4}[/tex] + 6 = 2 + 6 = 8
right side = x = 4
Since 8 ≠ 4 then x = 4 is an extraneous solution
x = 9
left side = [tex]\sqrt{9}[/tex] + 6 = 3 + 6 = 9
right side = x = 9
Thus the solution is x = 9 → B
