Find the solution (s) to x2 - 16x+64 = 0.

O

A. x = 8 only

B. X = 8 and x = - 8

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Ο

" C. χ = 4 and x = 16

Ο

D. X = - 2 and x = 32

A. x = 8 only

Step-by-step explanation:

x² - 16x + 64 = 0

The above equation is a quadratic equation, and can be solve by either formula method or factorization method or completing the square method.

We will be solving using the factorization method;

x² - 16x + 64 = 0

We are going to find two numbers such that its sum is equal to - 16 and its product is 64

The two numbers are; - 8 and - 8

-8 + (-8) = - 16

and - 8 (-8) = 64

We will replace - 16x by - 8x and - 8x

x² - 16x + 64 = 0

x² - 8x - 8x + 64 = 0

(x² - 8x) ( - 8x + 64) = 0

In the first parenthesis, x is common so we will factor out x while in the second parenthesis - 8 is common and it will be factored out.

That is;

x (x - 8) - 8 (x - 8) = 0

(x-8) (x-8) = 0

x - 8 = 0

Add 8 to both-side

x - 8 + 8 = 0 + 8

x = 8

Therefore x = 8 only

A

Step-by-step explanation:

Given

x² - 16x + 64 = 0 ← left side is a perfect square and factors as

(x - 8) ² = 0, thus

x - 8 = 0 ⇒ x = 8 with multiplicity 2

Thus x = 8 is the only solution → A