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24 December, 14:44

Use completing the square to solve for x in the equation (x+7) (x-9) = 25.

x = - 4 or 6

O O

x = - 2 or 14

X=1789

X=1187

O

+1
Answers (1)
  1. 24 December, 17:35
    +1
    x = 1 ±√89

    Step-by-step explanation:

    We have the equation:

    (x+7) (x-9) = 25

    Using distributive property:

    x (x-9) + 7 (x-9) = 25

    x² - 9x + 7x - 63 - 25 = 0

    x² - 2x - 88 = 0

    To complete squares we need to add and subtract 1, as follows:

    x² - 2x - 88 + 1 - 1 = 0

    x² - 2x + 1 - 88 - 1 = 0 (this is a perfect square)

    (x - 1) ² - 89 = 0

    Solving for x:

    (x - 1) ² = 89

    x - 1 = ±√89

    x = 1 ±√89
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