Question

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

Answer 1

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.

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`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)`