Help ASAP!!! Please show all work!!!!!!! Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer. √(x+7) -1=x\\

Question

Help ASAP!!! Please show all work!!!!!!!

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.


`√(x+7) -1=x\\`

Answer 1

`\bf\huge x=2`

Explanation:

Given that :

• 
  `√(x+7) -1=x\\`

to find :

• 
  `√(x+7) -1=x\\`

explanation :

⟼
`√(x+7) -1=x\\`

⟼ √x + 7 = x + 1

⟼ x + 7 = x² + 2x + 1

⟼ x + 7 - x² - 2x - 1 = 0

⟼ -x + 6 -x² = 0

⟼ x² + x - 6 = 0

⟼ (x-2) (x+3) = 0

⟼ x = 2 and x = -3

When x = -3 the original equation √x+7-1 = x does not hold true. We will drop x = -3 from the solution set.

Therefore,

⟼ x = 2.

verification :

⟼ let take x = 2

⟼
`√(x+7) -1=x\\`

⟼ √2+7 - 1 = 2

⟼ √9 - 1 = 2

⟼ 3 - 1 = 2

⟼ 2 = 2

hence verified ☑️

Answer 2

x = 2 and x = -3

Explanation:

We need to find the value of x in the below expression.

`√(x+7) -1=x`

Adding 1 to both sides,

`√(x+7) -1+1=x+1\\\\√(x+7)=x+1`

Squaring both sides,

`x+7=(x+1)^2\\\\x+7=x^2+1+2x\\\\x^2+1+2x-x-7=0\\\\x^2+x-6=0\\\\x=2\ and\ -3`

Hence, this is the required solution.