Question

(x–7)²–16=0 , Solve the given equation using the method of factorization.

Answer 1

(x – 7)² – 16 = 0

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write 16 as 4²:

(x – 7)² – 4² = 0

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Applying a² - b² = ( a + b) (a - b):

(x – 7 + 4) (x - 7 - 4) = 0

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Combine like terms:

(x – 3) (x - 11) = 0

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Apply zero product property:

( x - 3) = 0 or ( x - 11) = 0

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Solve x:

x = 3 or x = 11

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Answer: x = 3 or 11

Answer 2

( x - 7) ^2 - 16 = 0

=> x^2 - 14x + 49 - 16 = 0

=> x^2 - 14x + 33 = 0

=> x^2 - 3x - 11x + 33 = 0

=> x ( x - 3) - 11(x - 3) = 0

=> ( x - 3) (x - 11) = 0

x = 3 and 11