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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work. a^2 - 12a + 35 = 0       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

a%5E2-12a%2B35=0 Start with the given equation.


Notice that the quadratic a%5E2-12a%2B35 is in the form of Aa%5E2%2BBa%2BC where A=1, B=-12, and C=35


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


a+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


a+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%281%29%2835%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-12, and C=35


a+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%281%29%2835%29+%29%29%2F%282%281%29%29 Negate -12 to get 12.


a+=+%2812+%2B-+sqrt%28+144-4%281%29%2835%29+%29%29%2F%282%281%29%29 Square -12 to get 144.


a+=+%2812+%2B-+sqrt%28+144-140+%29%29%2F%282%281%29%29 Multiply 4%281%29%2835%29 to get 140


a+=+%2812+%2B-+sqrt%28+4+%29%29%2F%282%281%29%29 Subtract 140 from 144 to get 4


a+=+%2812+%2B-+sqrt%28+4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


a+=+%2812+%2B-+2%29%2F%282%29 Take the square root of 4 to get 2.


a+=+%2812+%2B+2%29%2F%282%29 or a+=+%2812+-+2%29%2F%282%29 Break up the expression.


a+=+%2814%29%2F%282%29 or a+=++%2810%29%2F%282%29 Combine like terms.


a+=+7 or a+=+5 Simplify.


So the solutions are a+=+7 or a+=+5


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

a%5E2+-+12a+%2B+35+=+0

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:

x%5E2+-+12x+%2B+35+=+0

a=1, b=-12, c=35

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



x+=+%2812+%2B-+sqrt%28144-140%29+%29%2F2+

x+=+%2812+%2B-+sqrt%284%29+%29%2F2+

x+=+%2812+%2B-+2+%29%2F2+

Using the +

x+=+%2812+%2B+2+%29%2F2+=14%2F2=7

Using the -

x+=+%2812+-+2+%29%2F2+=10%2F2=5

There are two solutions 7 and 5

Now we switch back to a from x, and get

a = 7 and a = 5.

Edwin