Answer:
x = 36
Step-by-step explanation:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
Subtract x and 36 from both sides.
[tex] -12\sqrt{x} = -x - 36 [/tex]
Divide both sides by -1.
[tex] 12\sqrt{x} = x + 36 [/tex]
Square both sides.
[tex] 144x = x^2 + 72x + 1296 [/tex]
Subtract 144x from both sides.
[tex] 0 = x^2 - 72x + 1296 [/tex]
Factor the right side.
[tex] 0 = (x - 36)^2 [/tex]
[tex] x - 36 = 0 [/tex]
[tex] x = 36 [/tex]
Since the solution of the equation involved squaring both sides, we musty check the answer for possible extraneous solutions.
Check x = 36:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
[tex] 36 - 12\sqrt{36} + 36 = 0 [/tex]
[tex] 36 - 12\times 6 + 36 = 0 [/tex]
[tex] 36 - 72 + 36 = 0 [/tex]
[tex] 0 = 0 [/tex]
Since 0 = 0 is a true statement, the solution x = 36 is a valid solution.
