SOLUTION: 20a squared + 39a + 8 factor out completely

Algebra.Com
Question 656705: 20a squared + 39a + 8
factor out completely
Found 3 solutions by MathLover1, lynnlo, Alan3354:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form


Start with the given equation



Subtract from both sides



Factor out the leading coefficient



Take half of the x coefficient to get (ie ).


Now square to get (ie )





Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation




Now factor to get



Distribute



Multiply



Now add to both sides to isolate y



Combine like terms




Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation we get:


Graph of . Notice how the vertex is (,).



Notice if we graph the final equation we get:


Graph of . Notice how the vertex is also (,).



So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.
Answer by lynnlo(4176)   (Show Source): You can put this solution on YOUR website!
did you mean to put something in front of your + sign
i did it another way and got
59a+8
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
20a squared + 39a + 8
factor out completely
-----------------

That can't be factored with integers --> prime
------------------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=881 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -0.232958896017209, -1.71704110398279. Here's your graph:
RELATED QUESTIONS

Factor completely. z squared + 2z -... (answered by josmiceli)
Factor completely. -3s squared - 10s +... (answered by jim_thompson5910)
factor completely. x squared + 2xy + 2x + y squared + 2y -... (answered by mananth)
factor out completely 35xy-5x-56y+8 (answered by jim_thompson5910)
Factor the polynomial completely. -3s squared - 10s +... (answered by checkley71)
Factor the following polynomial completely. -3s... (answered by Fombitz)
How do you factor out m(squared)- 3mn - 10n(squared) Completely lost !! (answered by Alan3354,rfer)
Factor completely k squared +... (answered by stanbon)
Factor completely. x squared - 6xy - 16y... (answered by jim_thompson5910)