We need to determine the value of `x ` in `x-6sqrt(x)=-8`
First, we isolate the term containing square root. So we have
Then if we square both sides, we get
By using FOIL method and further simplifying
`36x = x^2+16x+64`
By zero product property, the solution in the given equaiton is either `x=16` or `x=4` .
The equation `x-6x^(1/2)=-8` has to be solved for x.
Let `x^(1/2)=t` , then `x=t^2`
The given equation reduces to:
To solve for `t` , put each of the terms equal to zero.
When `t=4, x=t^2`
When `t=2, x=t^2`
Therefore, the values of x for which the equation `x-6x^(1/2)=-8` holds good are 2 and 4.