SOLUTION: Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work. a^2 - 12a + 35 = 0

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Question 299581: Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work.
a^2 - 12a + 35 = 0

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given equation.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "a":


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the solutions are or


Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!



Since the quadratic formula itself contains the letter a,
we must avoid confusion between the two uses for a.  
So let's use another letter besides a.  Let's substitute x
for a:



, , 











Using the +



Using the -



There are two solutions 7 and 5

Now we switch back to a from x, and get

a = 7 and a = 5.

Edwin

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