No.3
Solve for x:
6+sqrt(x)=x
Subtract 6 from both sides:
sqrt(x)=x-6
Raise both sides to the power of two:
x=(x-6)^2
Expand out terms of the right hand side:
x=x^2-12 x+36
Subtract x^2-12 x+36 from both sides:
-x^2+13 x-36=0
The left hand side factors into a product with three terms:
-(x-9) (x-4)=0
Multiply both sides by -1:
(x-9) (x-4)=0
Split into two equations:
x-9=0 or x-4=0
Add 9 to both sides:
x=9 or x-4=0
Add 4 to both sides:
x=9 or x=4
6+sqrt(x) ⇒ 6+sqrt(4) = 8
x ⇒ 4 = 4:
So this solution is incorrect
6+sqrt(x) ⇒ 6+sqrt(9) = 9
x ⇒ 9 = 9:
So this solution is correct
The solution is:
Answer: | x=9