factor:

x squared +14x+49

It's a perfect square of (x + _)^2

See if you can fill in the blank

Factor:X^2 + 14X + 49. 49 = 1*49 = 7*7

Try 1 and 49 in your factored equation:
( X + 1 )*(X + 49). The product of the two binomials does not equal the original equation, Therefore, 1 and 49 is incorrect. Try 7 and 7:(X+7)*(X+7)=
X^2 + 14X +49. Yes!

Problem:(X+ )^2. The results will be a perfect square regardless of what number you put in the blank, because you remove the parenthesis by squaring the contents.(X+2)^2=X^2+4X+4.(X+3)^2=X^2+6X+9.Both trinominals are perfect squares.

To factor the quadratic expression \(x^2 + 14x + 49\), you can use the quadratic formula or the technique of factoring by finding two numbers whose sum is \(14\) and whose product is \(49\).

Let's use factoring by finding two numbers.

We need to find two numbers whose sum is \(14\) and whose product is \(49\). The numbers that satisfy these criteria are \(7\) and \(7\), because \(7 + 7 = 14\) and \(7 \times 7 = 49\).

Now, we can rewrite the middle term \(14x\) using these two numbers as \(7x + 7x\).

\[x^2 + 7x + 7x + 49\]

Next, we group the terms and factor by grouping.

\[x(x + 7) + 7(x + 7)\]

Notice that we have a common factor of \((x + 7)\) in both terms. We can factor it out.

\[(x + 7)(x + 7)\]

Finally, we can write the factored form of the quadratic expression as \((x + 7)^2\).