Question

Solve (x-4)2 = 5.
O A. X=-4125
B. x=51-4
C. X=41-15
O D. x=9 and x=-1

Answer 1

x = 4 plus or minus sqrt(5).

Explanation:

(x - 4)^2 = 5

x^2 - 4x - 4x + 16 = 5

x^2 - 8x + 11 = 0

Now, we can use the formula -b plus or minus sqrt(b^2 - 4ac) / 2a to find what x is equal to.

(--8 plus or minus sqrt((-8)^2 - 4 * 1 * 11)) / 2 * 1

= (8 plus or minus sqrt(64 - 44)) / 2

= (8 plus or minus sqrt(20)) / 2

= (8 plus or minus 2 * sqrt(5)) / 2

= 4 plus or minus sqrt(5)

And there's your answer! x = 4 + sqrt(5) and x = 4 - sqrt(5).

Hope this helps!