SOLUTION: Hello, These are the problems that I am having trouble with: Solve: 1. -3x^2 + 5x - 1 = 0 2. x^2 + 6x + 6 = 0 Please and thanks!

Algebra ->  Systems-of-equations -> SOLUTION: Hello, These are the problems that I am having trouble with: Solve: 1. -3x^2 + 5x - 1 = 0 2. x^2 + 6x + 6 = 0 Please and thanks!      Log On


   

Question 479537: Hello,
These are the problems that I am having trouble with:
Solve:
1. -3x^2 + 5x - 1 = 0
2. x^2 + 6x + 6 = 0
Please and thanks!
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1. -3x^2 + 5x - 1 = 0
3x2-5x+1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%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=%28-5%29%5E2-4%2A3%2A1=13.

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

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+1.43425854591066
x%5B2%5D+=+%28-%28-5%29-sqrt%28+13+%29%29%2F2%5C3+=+0.232408120756002

Quadratic expression 3x%5E2%2B-5x%2B1 can be factored:
3x%5E2%2B-5x%2B1+=+3%28x-1.43425854591066%29%2A%28x-0.232408120756002%29
Again, the answer is: 1.43425854591066, 0.232408120756002. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B1+%29








2. x^2 + 6x + 6 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B6+=+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=%286%29%5E2-4%2A1%2A6=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+-1.26794919243112
x%5B2%5D+=+%28-%286%29-sqrt%28+12+%29%29%2F2%5C1+=+-4.73205080756888

Quadratic expression 1x%5E2%2B6x%2B6 can be factored:
1x%5E2%2B6x%2B6+=+1%28x--1.26794919243112%29%2A%28x--4.73205080756888%29
Again, the answer is: -1.26794919243112, -4.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B6+%29
..