solve square root equation x=6[squareroot(x-2)-1]?
We'll impose the constraint of existence of the square root:
We'll add 2 both sides:
The interval of admissible values is [2 ; +infinite).
We'll re-write the given equation. We'll isolate 6sqrt(x-2) to the right side. For this reason, we'll add 6 both sides:
6+x = 6sqrt(x-2)
We'll square raise both sides. For squaring the binomial from the left side, we'll use the formula;
(a+b)^2 = a^2 + 2ab + b^2
36 + 12x + x^2 = 36(x-2)
x^2+12x+36 = 36x-72
We'll subtract 36x-72:
x^2 - 24x + 108 = 0
We'll apply the quadratic formula:
x1=[24+ sqrt (24^2-4*108)]/2
x1 = (24+12)/2
x1 = 36/2
Since both values belong to the interval [2 ; +infinite), we'll validate them as solutions of the given equation: x1 = 18 and x2 = 6.