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10 votes
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

User Ktdrv
by
7.2k points

1 Answer

8 votes

Answer:

-4 and 12

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

-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

User Tepu
by
8.9k points

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