SOLUTION: Explain each step involved in using the 'ac' method to factor the following: 8x^2 + 2x - 3

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Question 22383: Explain each step involved in using the 'ac' method to factor the following:
8x^2 + 2x - 3
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
First you need to set the equation to 0 so you get a quadratic
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B2x%2B-3+=+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=%282%29%5E2-4%2A8%2A-3=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C8+=+0.5
x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C8+=+-0.75

Quadratic expression 8x%5E2%2B2x%2B-3 can be factored:
8x%5E2%2B2x%2B-3+=+8%28x-0.5%29%2A%28x--0.75%29
Again, the answer is: 0.5, -0.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B2%2Ax%2B-3+%29

Hope this helps!