Question 589388: Please help me get the simplified answer to this equation:  So far I did -21sqrt(21)^2-4(4)(5)/2(4). This equals -21+sqrt(361) all over 8, -21-sqrt(361) all over 8. How do I simplify this answer?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
IN GENERAL:
If you have a calculator, see if the square root is an integer.
If the square root is not an integer, you need to write what’s inside the square root as a product where one of the factors is a square.
For example, if you know that  you can simplify 
You may realize that the number in the square root has one of the easy to detect squares (4, 9, 25) as a factor.
If you do not see another way, finding the prime factorization may help.
PRIME FACTORIZATION:
You try the primes: 1,2,3,5,7,11,13,17,19… until you get one that divides the number evenly, or one that squared is larger than the number.
If you find a prime that divides the number evenly, you keep on working on the quotient.
For example, if you are faced with :
You see that 2 does not divide it evenly (2 is not a prime factor of 3825).
You see that 3 divides 3825 evenly and the result is 1275.
You keep working on 1275, starting with 3.
You see that 3 divides 1275 evenly and the result is 425.
You keep working on 425, starting with 3.
You see that 3 does not divide it evenly, so you try 5 next.
You see that 5 divides 425 evenly and the result is 85.
You keep working on 85, starting with 5.
You see that 5 divides 85 evenly and the result is 17.
Now, 17 is a prime number, so you do not need to keep dividing.
Each number that divided evenly is a factor (some more than once), and youf final quotient (17) is also a factor.
Now you know that 
So
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