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10 March, 20:41

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

O

A. x = 8 only

B. X = 8 and x = - 8

Ο

Ο

" C. χ = 4 and x = 16

Ο

D. X = - 2 and x = 32

+1
Answers (2)
  1. 10 March, 22:59
    0
    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
  2. 11 March, 00:09
    0
    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
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