Answer:
x=1
x=11
Explanation:
4(x-6)²-3=97
Add 3 to each side
4(x-6)²-3+3=97+3
4(x-6)²=100
Divide each side by 4
4/4(x-6)²=100/4
(x-6)²=25
Take the square root of each side
sqrt(4(x-6)²)=sqrt(25)
x-6 = ±5
Separating into two equations
x-6 = 5 x-6 = -5
Add 6 to each side
x-6+6 = 5+6 x-6+6 = -5+6
x=11 x=1
The two solutions are 1, 11