SOLUTION: how many solutions are there to this equation -0.2x^2+12x+11=0 and how do you know?

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Question 276030: how many solutions are there to this equation -0.2x^2+12x+11=0 and how do you know?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
there are two solutions and i know because I am smart.
The Discriminant tells you.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.2x%5E2%2B12x%2B11+=+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=%2812%29%5E2-4%2A-0.2%2A11=152.8.

Discriminant d=152.8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+152.8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+152.8+%29%29%2F2%5C-0.2+=+-0.903074280724887
x%5B2%5D+=+%28-%2812%29-sqrt%28+152.8+%29%29%2F2%5C-0.2+=+60.9030742807249

Quadratic expression -0.2x%5E2%2B12x%2B11 can be factored:
-0.2x%5E2%2B12x%2B11+=+-0.2%28x--0.903074280724887%29%2A%28x-60.9030742807249%29
Again, the answer is: -0.903074280724887, 60.9030742807249. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.2%2Ax%5E2%2B12%2Ax%2B11+%29