SOLUTION: Determine the solutions to the quadratic equation -10x2 + 30x - 20 = 0.

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Question 372009: Determine the solutions to the quadratic equation -10x2 + 30x - 20 = 0.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
-10x%5E2+%2B+30x+-+20+=+0
When solving quadratic equations you first want one side of the equation to be a zero. Your equation already has a zero on one side so we can go on to the next step. After you have a zero on one side, you either factor the other side or use the Quadratic Formula. This equation factors fairly easily. First we will factor out the Greatest Common Factor. (Looking ahead, I am going to factor out -10 instead of 10 because it will make the next step easier):
%28-10%29%28x%5E2+-3x+%2B2%29+=+0
The trinomial (which as a positive squared term because I factored out -10 instead of 10) is easily factored:
%28-10%29%28x-2%29%28x-1%29+=+0
Once we have the equation factored we use the Zero Product Property. This property tells us that this (or any) product can be equal to zero only if one (or more) of the factors is zero. So
-10 = 0 or x-2 = 0 or x-1 = 0
The first equation is impossible. But we can solve the other two:
x = 2 or x = 1