SOLUTION: I really need help with this problem! x^2 + 10x + 7 = 0

Question 896527: I really need help with this problem!

x^2 + 10x + 7 = 0
Found 2 solutions by JulietG, richwmiller:
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
Are you sure you've written the problem correctly?
There is no solution with rational numbers as written.
However, if it's x^2+7x+10, then it's simple factoring
(x+5)(x+2) = x^2+7x+10
X = -5,-2
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
First we try to factor.

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :

1,7

-1,-7

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .

1*7 = 7
(-1)*(-7) = 7

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number Second Number Sum
1 7 1+7=8
-1 -7 -1+(-7)=-8

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

then we use the quadratic_formula

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=10, and c=7

Square 10 to get 100

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

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