Which quadratic equation is equivalent to (x - 4)² - (x - 4) - 6 = 0?

Solution:

(x - 4)² - (x - 4) - 6 = 0 [Given]

Expanding using the formula (a - b)² = a² + b² - 2ab

x² + 16 - 8x - x + 4 - 6 = 0

By further calculation

x² - 9x + 14 = 0

Using the formula

x = [-b ± √(b² - 4ac)]/2a

Here a = 1, b = -9 and c = 14

Substituting it in the formula

x = [-(-9) ± √((-9)² - 4 (1) (14))]/2 (1)

x = [9 ± √(81 - 56)]/2 

So we get

x = [9 ± √25]/2 

x = (9 + 5)/2 = 14/2 = 7

x = (9 - 5)/2 = 4/2 = 2

Therefore, the quadratic equation equivalent to (x - 4)² - (x - 4) - 6 = 0 is x² - 9x + 14 = 0.

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Which quadratic equation is equivalent to (x - 4)² - (x - 4) - 6 = 0?

Summary:

The quadratic equation which is equivalent to (x - 4)² - (x - 4) - 6 = 0 is x² - 9x + 14 = 0.