Part 6 of 8
(f) Fill in the blank to complete the square for the trinomial

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Part 6 of 8 (f) Fill in the blank to complete the square for the trinomial $$ x^{2}+20 x+\square $$

UpStudy AI · Accepted Answer

To complete the square for the trinomial $$ x^{2} + 20x + \square $$, we need to find a value to fill in the blank that makes it a perfect square trinomial.

1. Take the coefficient of $$ x $$, which is $$ 20 $$.
2. Divide it by $$ 2 $$: $$ \frac{20}{2} = 10 $$.
3. Square the result: $$ 10^2 = 100 $$.

Thus, the value to fill in the blank is $$ 100 $$.

So, the completed expression is:

$$
x^{2} + 20x + 100
$$

This can be factored as $$ (x + 10)^2 $$.
Fill in the blank with 100.

Part 6 of 8
(f) Fill in the blank to complete the square for the trinomial

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