Solving with Radicals. Help

Question

Could someone help me with this problem everyone seems to not understand what is being asked when I submitted this question before

 

x-1=√7-x

Answer 1

As posted:

 

x-1 = √7 - x

add x to both sides

2x - 1 = √7

add 1 to both sides

2x = 1 + √7

divide both sides by 2

x = (1+√7)/2

 

If you left out a parenthesis and meant...

 

x-1 = √(7-x)

square both sides

(x-1)² = 7-x

x² - 2x + 1 = 7-x

x² -x - 6 = 0

 

To factor this look for factors of -6 that add to -1.

(-3)(2) = -6   and. -3+2=-1

 

(x-3)(x+2) = 0

x = 3 or x = -2

 

check:  x=3

3-1 = √(7-3)

2 = √4

2 = 2

 

check: x=-2

-2-1 = √(7-(-2))

-3 = √9

 

If we are dealing only with positive square roots

the answer is x=3