SOLUTION: Solve -x^2-3x+1=0 Thank you so much! I am a writing teacher and my kids need help with their math. Trying to find free help as a parent is really hard, but this site is such a g

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve -x^2-3x+1=0 Thank you so much! I am a writing teacher and my kids need help with their math. Trying to find free help as a parent is really hard, but this site is such a g      Log On


   

Question 1050907: Solve -x^2-3x+1=0
Thank you so much! I am a writing teacher and my kids need help with their math. Trying to find free help as a parent is really hard, but this site is such a great idea!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve -x^2-3x+1=0
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There's more than 1 way to do this.
This method always works.
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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 -1x%5E2%2B-3x%2B1+=+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=%28-3%29%5E2-4%2A-1%2A1=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+13+%29%29%2F2%5C-1+=+-3.30277563773199
x%5B2%5D+=+%28-%28-3%29-sqrt%28+13+%29%29%2F2%5C-1+=+0.302775637731995

Quadratic expression -1x%5E2%2B-3x%2B1 can be factored:
-1x%5E2%2B-3x%2B1+=+%28x--3.30277563773199%29%2A%28x-0.302775637731995%29
Again, the answer is: -3.30277563773199, 0.302775637731995. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-3%2Ax%2B1+%29