Question 648116: 4x squared-4x-99=0
Found 2 solutions by stanbon, Algebraic:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 4x squared-4x-99=0
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4x^2 - 4x - 99 = 0
Factor:
(2x-11)(2x+9) = 0
x = 11/2 or x = -9/2
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Cheers,
Stan H.
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Answer by Algebraic(50)  (Show Source):
You can put this solution on YOUR website! Original problem: 
We're going to be factoring this to extract the roots (what 'x' equals)
Step 1: We must find two numbers that when '4' and '-99' multiply, will divide to give you '-4' in the middle.
You have quite a few number of combinations:
The  can be broken up into
or
We know that '-99' has six factors, and these include:
1 x 99, 3 x 33, and 9 x 11
Step 2: Let's start trying to see what will work and not work (trial and error method)
We know that regardless of signs, none of the factors of '-99' will be able to multiply here to give you a '-4' in the middle using this equation:
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
Now that we know that the equation won't work, let's move on to the other equation that could possibly work..
Step 3: Let's start trying to see what will work and not work (trial and error method)
We know that '-99' has six factors, and these include:
1 x 99, 3 x 33, and 9 x 11
We know that regardless of signs, none of the factors of '-99' will be able to multiply here to give you a '-4' in the middle using this equation:
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Does not work, gives you  in the middle
 ---> Works!! Gives you  in the middle, which is equivalent to '-4x'
 ---> Does not work, gives you  in the middle
So.. now we know that the factored version of the equation you provided is:
To get the roots, you must set each parenthesis equal to zero like so..
Step 1: Set each parenthesis equal to zero
Step 2: Let's solve each one at a time
Subtract '9' from both sides to get the '2x' by itself
Divide both sides by '2' to get 'x' by itself
First root is
Step 3: Let's find the other root
Add '11' to both sides to get the '2x' by itself
Divide both sides by '2' to get the 'x' by itself
Second root is
So, the factored version of this equation is and its roots are and
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