SOLUTION: Solve by applying the Quadratic Formula. Show the work, so I can do my other problems. Thank you in advance. Q: 25b^2-30b-7=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve by applying the Quadratic Formula. Show the work, so I can do my other problems. Thank you in advance. Q: 25b^2-30b-7=0      Log On


   

Question 231511: Solve by applying the Quadratic Formula. Show the work, so I can do my other problems. Thank you in advance.
Q: 25b^2-30b-7=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
25b^2-30b-7=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 25x%5E2%2B-30x%2B-7+=+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=%28-30%29%5E2-4%2A25%2A-7=1600.

Discriminant d=1600 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--30%2B-sqrt%28+1600+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+1600+%29%29%2F2%5C25+=+1.4
x%5B2%5D+=+%28-%28-30%29-sqrt%28+1600+%29%29%2F2%5C25+=+-0.2

Quadratic expression 25x%5E2%2B-30x%2B-7 can be factored:
25x%5E2%2B-30x%2B-7+=+%28x-1.4%29%2A%28x--0.2%29
Again, the answer is: 1.4, -0.2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+25%2Ax%5E2%2B-30%2Ax%2B-7+%29

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The solver uses x, just sub b for x.