SOLUTION: The problem is 6-sqrt x = x. I can figure out that the answer is 4 but what would be the equation?

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Question 37477: The problem is 6-sqrt x = x. I can figure out that the answer is 4 but what would be the equation?
Answer by Cintchr(475) About Me  (Show Source):
You can put this solution on YOUR website!
+6+-+sqrt%28x%29+=+x+
move the sqrt and the x to opposite sides so that the root is positive
+6+-+x+=+sqrt%28x%29+
square both sides
+%286-x%29%5E2+=+%28sqrt%28x%29%29%5E2+
Foil out the right side
+36+-+12x+%2B+x%5E2+=+%28sqrt%28x%29%29%5E2+
The sqrt and the square on the right cancel each other out
+36+-+12x+%2B+x%5E2+=+x+
Move the x to the left
+36+-+13x+%2B+x%5E2+=+0+
put in descending order
+x%5E2+-+13x+%2B+36+=+0+
factor
+%28x-4%29%28x-9%29=0+
set both parts equal to 0
+x-4+=+0+ and +x-9=0+
+x+=+4+ and +x+=+9+
You got 4 ...
now ... keep in mind that when you find a root ... you not only get a possitive number but a neagative as well.
plugging in 9 ....
+6+-+sqrt%289%29+=+9+
The sqrt of 9 is 3 but also -3
+6+-+-3+=+9+
+6+%2B+3+=+9+
+9+=+9+