16 should be added to both sides of the equation to complete the square.
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.
Given the equation x² - 8x = 9, solving using completing the square method:
x² - 8x = 9
Add to both sides the square of half of the coefficient of x, that is 16:
x² - 8x + 16 = 9 + 16
(x - 4)² = 25
Take square root of both sides:
x - 4 = ±5
x = 4 ± 5
x = 4 + 5 or x = 4 - 5
x = 9 or x = -1
Hence, 16 should be added to both sides of the equation to complete the square.
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