Question 206019This question is from textbook Intermediate Algebra
: x^2 - 3x^1/2 - 10 = 0
This question is from textbook Intermediate Algebra
Answer by mickclns(59)   (Show Source):
You can put this solution on YOUR website!  notation housekeeping
 multiply both sides by 2 to get rid of the fraction
There are various ways of factoring a quadratic (if it factors, which this does, because  is a perfect square). I like this way:
First multiply the coefficient of the  term, 2, by the constant term, -20, to get -40. Now you want to find two numbers that multiply to this number, -40, and that add to the coefficient of x, in this case -3. The two numbers are -8 and 5.
Now you put those two numbers into the blanks in  (and it doesn't matter which number in which blank):
Case 1:  . Now factor out whatever you can out of the first two terms and factor out whatever you can out of the last two terms:
 . Notice both terms have a factor of x-4 which you can factor out:
 .
Case 2:  . Now factor out whatever you can out of the first two terms and factor out whatever you can out of the last two terms:
 . Again, both terms have a factor, 2x + 5 this time, which you can factor out:
 .
In both cases the factors are the same except in opposite order, which makes not a whit of difference.
It is a good idea to multiply out (FOIL) to make sure you have factored correctly
Now we use the zero product property which says that if a product of a bunch of numbers is 0 then one of the numbers must be 0, which is what allows us to set each of the factors to 0.
 -->  or  , so  or  .
Now it's a good idea to check your answers to make sure they work, by plugging them in (one at a time) for x in the ORIGINAL equation (I will do one, you can do the other):
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 Yes!
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