SOLUTION: I can not seem to be able to factor this 2w(4w+1)=1

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Question 203629: I can not seem to be able to factor this
2w(4w+1)=1
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
2w%284w%2B1%29=1
8w%5E2+%2B+2w+=+1
8w%5E2+%2B+2w+-+1+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 8w%5E2%2B2w%2B-1+=+0) has the following solutons:

w%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=%282%29%5E2-4%2A8%2A-1=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+36+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%282%29%2Bsqrt%28+36+%29%29%2F2%5C8+=+0.25
w%5B2%5D+=+%28-%282%29-sqrt%28+36+%29%29%2F2%5C8+=+-0.5

Quadratic expression 8w%5E2%2B2w%2B-1 can be factored:
8w%5E2%2B2w%2B-1+=+8%28w-0.25%29%2A%28w--0.5%29
Again, the answer is: 0.25, -0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B2%2Ax%2B-1+%29




plot is here --> http://www24.wolframalpha.com/input/?i=2w(4w%2B1)%3D1