SOLUTION: How do you solve these two equations using the quadratic formula? 2x^2-7x=-5....How do I get an A,B,and C if there is only A and B? 6x^2=2x+1....Do I switch this around to make

Algebra ->  Equations -> SOLUTION: How do you solve these two equations using the quadratic formula? 2x^2-7x=-5....How do I get an A,B,and C if there is only A and B? 6x^2=2x+1....Do I switch this around to make      Log On


   

Question 713868: How do you solve these two equations using the quadratic formula?
2x^2-7x=-5....How do I get an A,B,and C if there is only A and B?
6x^2=2x+1....Do I switch this around to make A, B and C?
Answer by BGutridge(15) About Me  (Show Source):
You can put this solution on YOUR website!
1) 2x^2-7x=-5 Set the equation equal to zero. That leaves 2x^2-7x+5=0. Then
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-7x%2B5+=+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=%28-7%29%5E2-4%2A2%2A5=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+9+%29%29%2F2%5C2+=+2.5
x%5B2%5D+=+%28-%28-7%29-sqrt%28+9+%29%29%2F2%5C2+=+1

Quadratic expression 2x%5E2%2B-7x%2B5 can be factored:
2x%5E2%2B-7x%2B5+=+2%28x-2.5%29%2A%28x-1%29
Again, the answer is: 2.5, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-7%2Ax%2B5+%29


2) 6x^2=2x+1 Set the equation equal to zero, which gives 6x^2-2x-1=0. Then
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-2x%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=%28-2%29%5E2-4%2A6%2A-1=28.

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

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+28+%29%29%2F2%5C6+=+0.607625218510765
x%5B2%5D+=+%28-%28-2%29-sqrt%28+28+%29%29%2F2%5C6+=+-0.274291885177432

Quadratic expression 6x%5E2%2B-2x%2B-1 can be factored:
6x%5E2%2B-2x%2B-1+=+6%28x-0.607625218510765%29%2A%28x--0.274291885177432%29
Again, the answer is: 0.607625218510765, -0.274291885177432. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-2%2Ax%2B-1+%29


Sorry that that 2nd one doesn't have a simple answer.