Solve by using appropriate substitution?

Question

Solve equation by making an appropriate substitution.
(x is the only number under the radical sign)

x + 7√ x - 8 = 0

Answer 1

Let u^2 = x
Thus u^2 + 7u - 8 = 0
Now factor: (u+8)(u-1)=0
so u = -8 or 1.
but u^2 cannot be negative, so no x will work for -8, but x = 1 satisfies u^2 = 1.
Thus x=1 is your only solution.

Answer 2

Let y^2 = x
Then y^2 +7y - 8 = 0
(y+8)(y-1) = 0
y=1 or y= -8
x= y^2 so x = 1^2 = 1 and x = (-8)^2 = 64
The solution x=64 is rejected as it does not satisfy the equation. Hence x =1 is the only solution.

Answer 3

substitue x by y^2
y^2 + 7y - 8 =0
=> y=-8,1
But the negative y is not accepted, since sqrtx is positive, so y should be positive. So x=1

Answer 4

x + 7√ x - 8 = 0
Let y = √ x
Then y^2 + 7y - 8 = 0
Factor
(y+8)(y-1) = 0
y = -8; +1
x = √ -8; √ 1
x = +2i√ 2; -2i√ 2; 1; -1