What are the solutions to the following equation? (x−4)2=64
Question 3 options:

-68 and -60

60 and 68

-4 and 12

-12 and 4

-4 and 12

Step-by-step explanation:

(x-4)² is the same as (x-4)(x-4)

now we have

(x-4)(x-4) = 64

expand (x-4)(x-4)

x²-4x-4x+16 which is simplified to x²-8x+16

equate to 64

x²-8x+16 = 64

subtract 64 on both sides

x²-8x+16-64 = 0

x²-8x-48 = 0

to find x

what two numbers multiply to give -48 and add to give -8? That is -12 and 4 which we can write in brackets

(x-12)(x+4) = 0

equate each bracket to 0 to find x

x-12 = 0 and x+4 = 0

x = 12 and x = -4

step-by-step explanation: