SOLUTION: Solve -x^2-3x+1=0 with clear steps so I can learn please! Thank you!

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Question 1051090: Solve -x^2-3x+1=0 with clear steps so I can learn please! Thank you!
Found 3 solutions by Alan3354, ikleyn, Boreal:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
-x^2-3x+1=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 -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

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve -x^2-3x+1=0 with clear steps so I can learn please! Thank you!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` 

The equation is equivalent to 

x%5E2+%2B+3x+-1 = 0.   ( After multiplying both sides by (-1) )

Apply the quadratic formula

x%5B1%2C2%5D = %28-3+%2B-+sqrt%283%5E2+-+4%2A1%2A%28-1%29%29%29%2F2 = %28-3+%2B-+sqrt%289%2B4%29%29%2F2 = %28-3+%2B-+sqrt%2813%29%29%2F2.

Thus  x%5B1%5D = %28-3+%2B+sqrt%2813%29%29%2F2, x%5B2%5D = %28-3+-+sqrt%2813%29%29%2F2.

On quadratic formula, see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.


Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
-x^2-3x+1=0
change the sign of everything (multiply the entire equation by -1) to make the coefficient of the x^2 positive. That makes it a LOT easier.
x^2+3x-1=0
This does not factor.
Use the quadratic formula
x=(1/2)(-b+/-sqrt(b^2-4ac)
x=(1/2)(-3+/- sqrt (9+4))
x=(1/2)(-3+/-sqrt (13))
numerically, this is -3.31 and +0.31
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C-x%5E2-3x%2B1%29