Answer:
x = 6 and x = 11.
Step-by-step explanation:
sqrt(x - 2) + 8 = x
sqrt(x - 2) = x - 8
(sqrt(x - 2))^2 = (x - 8)^2
x - 2 = x^2 - 16x + 64
x^2 - 16x + 64 = x - 2
x^2 - 17x + 66 = 0
We can use the discriminant to find whether there are solutions to the equation.
b^2 - 4ac; where a = 1, b = -17, and c = 66.
(-17)^2 - 4 * 1 * 66
= 289 - 264
= 25
Since the discriminant is positive, we know there are two valid solutions to the equation.
x^2 - 17x + 66 = 0
(x - 6)(x - 11) = 0
The solutions are when x - 6 = 0 and x - 11 = 0.
x - 6 = 0
x = 6
x - 11 = 0
x = 11
Hope this helps!
