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
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
