SOLUTION: I am having a problem with this one: Solve using the quadratic formula. 2x^2-1=6x

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: I am having a problem with this one: Solve using the quadratic formula. 2x^2-1=6x      Log On


   

Question 83532: I am having a problem with this one:
Solve using the quadratic formula. 2x^2-1=6x
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-1=6x Start with the given equation

2x%5E2-1-6x=0 Subtract 6x from both sides

2x%5E2-6x-1=0 Rearrange in ax%5E2%2Bbx%2Bc form

Now use the quadratic formula to solve for x

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-6x%2B-1+=+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=%28-6%29%5E2-4%2A2%2A-1=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+44+%29%29%2F2%5C2+=+3.1583123951777
x%5B2%5D+=+%28-%28-6%29-sqrt%28+44+%29%29%2F2%5C2+=+-0.1583123951777

Quadratic expression 2x%5E2%2B-6x%2B-1 can be factored:
2x%5E2%2B-6x%2B-1+=+2%28x-3.1583123951777%29%2A%28x--0.1583123951777%29
Again, the answer is: 3.1583123951777, -0.1583123951777. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B-1+%29