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Hey there!
Use the distributive property at first.
(x + 7)(x - 9) = 25
x (x - 9) + 7 (x - 9) = 25
x² - 9x + 7x - 9 = 25
x² - 2x - 9 = 25
x² - 2x = 25 + 9
x² - 2x = 88
Now make the LHS of a equation a perfect square by adding the square of -1 to both the sides.
x² - 2x + (-1)² = 88 + (-1)²
x² - 2x + 1 = 88 + 1
By factorising the terms in LHS & adding the terms in RHS..
(x - 1)² = 89
Take the square root of both the sides.
√(x - 1)² = √(89)
By simplifying..we will get the answer as...
x - 1 = +/- √89
Adding 1 to both the sides...the values of x will be :-
x = √89 + 1
x = 1 - √89
Hope it helps ya!