Question

How do i solve for this help please \sqrt(x+5) = \sqrt(x)+1

Answer 1

`\boxed{x=4}`

Explanation:

`√(x+5) = √(x)+1`

Take the square on both sides.

`x+5=( √(x)+1)^2`

Expand brackets.

`x+5=( √(x)+1) ( √(x)+1)`

`x+5= √(x) ( √(x)+1) +1 ( √(x)+1)`

`x+5= x+ √(x)+ √(x)+1`

`x+5= x+ 2 √(x)+1`

Subtract 2√x, x, and 5 on both sides.

`x- 2 √(x) -x= 1-5`

`-2 √(x) = -4`

Cancel negative signs.

`2√(x) = 4`

Divide both sides by 2.

`√(x) =2`

Square both sides.

`x=2^2`

`x=4`

Check if the solution in the equation works.

`√(x+5) = √(x)+1`

Let
`x=4`

`√(4+5) = √(4)+1`

`√(9) = 2+1`

`3=3`

The value of x as 4 works in the equation.

Answer 2

x=4

Explanation:

sqrt(x+5) = sqrt(x)+1

Square each side

(sqrt(x+5))^2 = (sqrt(x)+1)^2

x+5 = (sqrt(x)+1)^2

Foil

x+5 = (sqrt(x)) ^2 + sqrt(x) + sqrt(x) + 1

x+5 = x + 2 sqrt(x) + 1

Subtract x from each side

5 = 2 sqrt(x) + 1

Subtract 1 from each sdie

4 = 2 sqrt(x)

Square each side

4^2 = (2 sqrt(x))^2

16 = 4 x

Divide by 4

16/4 = 4x/4

4 =x

Check to see if it is extraneous

sqrt(4+5) = sqrt(4)+1

sqrt(9) = sqrt(4) +1

3 = 2+1

3=3

It is a valid solution