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What would need to be added to both sides in order to complete the square in the following equation?

x² - 18x + 9 = 17?
a) 81
b) 13.5
c) 162
d) 4.5

User Vandna
by
8.6k points

1 Answer

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Final answer:

To complete the square for the equation x² - 18x + 9 = 17, you would add 81 to both sides, which is the square of half the coefficient of x (half of -18 is -9; -9 squared is 81).

Step-by-step explanation:

In order to complete the square for the equation x² - 18x + 9 = 17, we want to form a perfect square trinomial on the left side. This involves adding the square of half the coefficient of x to both sides. So, we take the coefficient of x, which is -18, divide it by 2 to get -9, and then square it to get 81. We will add 81 to both sides of the equation.

The equation with the complete square will look like this: x² - 18x + 81 = 17 + 81. After addition, the equation simplifies to (x - 9)² = 98. So the number you would need to add to both sides of the equation is 81.

User Shanmuga Raja
by
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