Question

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

Answer 1

Answer:

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

Answer 2

Answer:

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