SOLUTION: how do you factor 50g^2+40g+8

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Question 306304: how do you factor 50g^2+40g+8
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 50g%5E2+%2B+40g+%2B+8
I would start by reducing the equation. Everything is divisible by 2
2%2A%2825g%5E2+%2B+20g+%2B+4%29
Find the factors of 4: 1, 2, 2, 4
Find the factors of 25: 1, 5, 5, 25
Now since the 4 is positive that means that both factors contain both + signs or both - signs.
But since the 20g is positive, both factors can not contain negative signs.
Then you have to see which of your factors fit.
highlight%282%2A%285g+%2B+2%29%2A%285g+%2B+2%29%29
Then you can solve for g by setting the factor to 0 or using the quadratic equation.
5g+%2B+2+=+0
5g+=+-2
highlight_green%28g+=+-2%2F5%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 50x%5E2%2B40x%2B8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2840%29%5E2-4%2A50%2A8=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2840%29%29%2F2%5C50.
Expression can be factored: 50x%5E2%2B40x%2B8+=+50%28x--0.4%29%2A%28x--0.4%29

Again, the answer is: -0.4, -0.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+50%2Ax%5E2%2B40%2Ax%2B8+%29