SOLUTION: Hello! I was absent from my algebra lesson, and I have a queston on my homework.It asks that I solve the equasion. The equasion is -2h^2-28h-98 . I know so far that I need to put i

Question 414527: Hello! I was absent from my algebra lesson, and I have a queston on my homework.It asks that I solve the equasion. The equasion is -2h^2-28h-98 . I know so far that I need to put it in two different sets of parenthasees. So far, all I have written down is (-h ) (h ). Please help me, because I am very confused. Thank you!
Found 3 solutions by jim_thompson5910, ankor@dixie-net.com, josmiceli:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,7,49
-1,-7,-49

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

These factors pair up and multiply to .
1*49 = 49
7*7 = 49
(-1)*(-49) = 49
(-7)*(-7) = 49

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 49 1+49=50
7 7 7+7=14
-1 -49 -1+(-49)=-50
-7 -7 -7+(-7)=-14

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

Condense the terms.

--------------------------------------------------

So then factors further to

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

Answer:

So completely factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
solve the equation: -2h^2 - 28h - 98 = 0
You can greatly simplify this be dividing both sides by -2, then you have
h^2 + 14h + 49 = 0
this easily factors to:
(h + 7)(h + 7) = 0
so we have
h = -7
:
:
Check this in the original equation
-2(-7^2) - 28(-7) - 98 = 0
-2(49) + 196 - 98
-98 + 196 - 98 = 0 confirms our solution of h = -7

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
What you missed is the factoring of the equation. In order to
factor it, you need to find the roots. the roots are where the
graph of the equation intersects the x-axis. That is also
where , so I can say
Now set

Divide through by

One way to factor this is with the quadratic formula

Use this formula when the equation is in the form

Plug in these values:

and also

In this case you have a double root, both are
I can write them as:

and

Multiplying out,

So, I have found the 2 factors.
The graph of the equation is:

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