Answer:
x = 8 and x = 9
Step-by-step explanation:
[tex] \sqrt{x - 8} + 8 = x [/tex]
Isolate the radical and square both sides.
[tex] \sqrt{x - 8} = x - 8 [/tex]
[tex] (\sqrt{x - 8})^2 = (x - 8)^2 [/tex]
[tex] x - 8 = x^2 - 16x + 64 [/tex]
[tex] x^2 - 17x + 72 = 0 [/tex]
[tex] (x - 8)(x - 9) = 0 [/tex]
[tex] x - 8 = 0~~~or~~~x - 9 = 0 [/tex]
[tex] x = 8~~~or~~~x = 9 [/tex]
Since squaring both sides may introduce extraneous solutions, we check both of our solutions in the original equation.
Check x = 8:
[tex] \sqrt{8 - 8} + 8 = 8 [/tex]
[tex] \sqrt{0} + 8 = 8 [/tex]
[tex] 0 + 8 = 8 [/tex]
[tex] 8 = 8 [/tex]
8 = 8 is a true statement, so x = 8 is a solution.
Check x = 9:
[tex] \sqrt{9 - 8} + 8 = 9 [/tex]
[tex] \sqrt{1} + 8 = 9 [/tex]
[tex] 1 + 8 = 9 [/tex]
[tex] 9 = 9 [/tex]
9 = 9 is a true statement, so x = 9 is a solution.
Answer: x = 8 and x = 9
