What is x in (x-2)^2=64 ?

1 Answer
May 24, 2018

x=-6 or x=10

Explanation:

(x - 2)^2 = 64

The exponent 2 means that x-2 will multiply itself twice.

(x - 2)(x - 2) = 64

Use the distributive property on the left side

(x)(x) + (x)(-2) + (-2)(x) + (-2)(-2)=64

x^2 - 2x - 2x +4 = 64

x^2 - 4x + 4 = 64

Now we can subtract 64 from both sides

x^2 - 4x + 4 - 64 = 64 - 64

x^2 - 4x - 60 = 0

Then factorize the left side

(x + 6)(x-10)=0

Now we can set the factors equal to 0

x + 6 = 0 or x - 10 = 0

x = 0 - 6 or x = 0 + 10

x = -6 or x = 10 larr This is the final answer!