Factoring polynomials- x^2 + 49 = -14x?

Question

I'm more interested in finding the steps on how to get the answer rather than the answer.

by the way it's
x^2 + 49 = -14x

Answer 1

x^2 + 49 = -14x

Rearrange into normal quadratic form

x^2 +14x +49 = 0

You want to factor into (x + a)(x+b)
You know both signs are plus because all parts of the quadratic are positive.

So you want to find a & b such that a*b = 49 and a+b = 14.

To find this, you can:
1) Plug it into the quadratic formula
2) Think & find the number directly
3) plot it and look for the zero crossings.

In this case it's easy since 7*7 = 49 and 7+7 = 14

So the factorization is (x + 7)(x+7)

Answer 2

Bring everything over to one side
x^2 + 14x + 49 = 0

What are the factors of 14?
(1, 14) (2, 7)

Then you have to figure out combinations that will give you 49. The only thing here that divides into 49 is 7 and conveniently there are two of them. So you get:

(x + 7)(x + 7)

Answer 3

x^2 + 49 + 14 x = 0
Rearrange..

x^2 + 14x + 49

What times what=49..and the sum of those two factors adds up to 14?

(x+7)(x+7) = 0
(x+7)^2 = 0

x = -7

Answer 4

bring over to LHS
x^2 + 14x + 49 = 0
now I know that 49=7^2 and I see 14 = 2*7
(x+7)^2 = 0
so x = -7 is double root

Answer 5

x^2+14x+49=0 (x+7)^2

Answer 6

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

Answer 7

x^2 + 49 = -14x
x^2+14x+49 = 0
(x + ?)(x+?) =0
The ?'s must be two numbers which when added = 14 and when multiplied = 49.
Obviously the ?'s are both 7, so we have
(x+7)(x+7) = (x+7)^2

Answer 8

Make the whole equation on one side...so its x^2 + 14x + 49 = 0

Now...this is kindve a guess and check thing that you get better and better at.

Just by looking at this I knew it was
(x + 7)(x + 7)

You need to know that the numbers (7) need to add up to 14, and multiply to 49...7 is the obvious choice.

Answer 9

x^2 + 49 = -14x
x^2 + 14x + 49 = 0
(x + 7)(x + 7) = 0

The whole concept of factoring can be thought of like the reverse of the FOIL method. You want to find two factors that, when multiplied together completely, comes out like your original polynomial. Unfortunately, though, it requires a lot of trial and error, and I can't say there is any clear-cut, step-by-step way to factor polynomials.

The trick, though, is to look at the final constant, which in this case is 49, and try to list its factors (whether on paper or with practice in your head). At the same time, you also have to look at the coefficient of the middle term, which turns out to be 14 once I rearranged the terms, and figure out which of the factors of 49, when multiplied in the order of FOIL, will also give you 14. The way to do that is to consider the signs. In this case you have all positive signs separating the terms, so you know that within your factors you'll be adding. By working them out one at a time and trying to figure out which one works, you should find that 7, when added (7x + 7x), gives you your middle term, and when multiplied gives you your constant.

Like I said, there's is no definite way to reverse FOIL, but with practice it gets easier.

Answer 10

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