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Find the number to add to to make it a perfect square trinomial. Write that trinomial as the square of a binomial?

User Helado
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1 Answer

4 votes

Answer:

Divide the b parameter by 2 and rewrite it as the square of a binomial inserting the x, and the c as the half of b.

.
x^(2)+14x+49= (x+7)^(2)

Explanation:

1) Every perfect square trinomial can be written as the square of a binomial. For instance:


x^(2)+8x+16 = (x+4)^(2)\\x^(2)-7x+49=(x-7)^(2)\\x^(2)+24x+144= (x+12)^(2)

2) Firstly let's complete the square

2a. Find "c", the constant term by dividing "b"


x^(2)+14x\Rightarrow x^(2)+14x+7

2b. Square it


x^(2)+14x+7^(2)

3) Since we completed the square, then to write that trinomial as the square of a binomial :

Divide the b parameter by 2 and rewrite it as the square of a binomial inserting the x, and the c as the half of b.

.
x^(2)+14x+49= (x+7)^(2)

User Kota Mori
by
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