Solve for x square root (x+7) = 4-square root(x-1).

We'll re-write the
expression:

 sqrt(x+7) + sqrt(x-1) = 4
(1)

We'll multiply the adjoint expression of the left side,
to the both sides of the equation.

[sqrt(x+7) +
sqrt(x-1)]*[sqrt(x+7) - sqrt(x-1)]= 4*[sqrt(x+7) -
sqrt(x-1)]

We'll have as result of the product of the left
side, a difference of squares:

(a-b)(a+b) = a^2 -
b^2

We'll put a = sqrt(x+7) and b =
sqrt(x-1)

(x+7) - (x-1)= 4*[sqrt(x+7) -
sqrt(x-1)]

We'll remove the brackets from the left
side:

x + 7 - x +1= 4*[sqrt(x+7) -
sqrt(x-1)]

We'll combine and eliminate like
terms:

8 = 4*[sqrt(x+7) -
sqrt(x-1)]

We'll divide by 4 both
sides:

2= sqrt(x+7) - sqrt(x-1)
(2)

We'll add
(1)+(2):

 sqrt(x+7) + sqrt(x-1) + sqrt(x+7) - sqrt(x-1) =
6

We'll combine and eliminate like
terms:

2sqrt(x+7)= 6

We'll
divide by 2:

sqrt(x+7)=
3

We'll raise to square both
sides:

[sqrt(x+7)]^2= 92=
3^2

x+7= 9

x=
9-7

x=
2

We'll substitute x by 2
and we'll conclude that x= 2 is the solution of the
equation.