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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=13 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -3.30277563773199, 0.302775637731995. Here's your graph:
Answer by ikleyn(52781)   (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 

 = .   ( After multiplying both sides by (-1) )

Apply the quadratic formula

 =  =  = .

Thus   = ,  = .

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)   (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
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