Find one value of x that is a solution to the equation: (x^2-6) ^2=-3x^2+18

root 3 or root 6

Step-by-step explanation:

Let x^2 = y

(y-6) ^2 = - 3y+18

(y-6) (y-6) = - 3y+18

y^2-6y-6y+36 = - 3y+18

y^2-12y+36 = - 3y+18

y^2-12y+3y+36-18 = 0

y^2-9y+18 = 0

y^2-6y-3y+18=0

y (y-6) - 3 (y-6) = 0

(y-3) or (y-6) = 0

y-3 = 0 or y-6 = 0

y = 3 or 6

remember that y = x^2

x^2 = 6

x = root 6

x^2 = 3

x = root 3

x = root 3 or root 6