SOLUTION: x^2-3x = 4x -1 I can't do the problems that do not have an = 0. I tried to do this by putting the entire equation on the left of the =, and came up with x^2 -7x +1 = 0. But wi

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: x^2-3x = 4x -1 I can't do the problems that do not have an = 0. I tried to do this by putting the entire equation on the left of the =, and came up with x^2 -7x +1 = 0. But wi      Log On


   

Question 78141: x^2-3x = 4x -1 I can't do the problems that do not have an = 0. I tried to do this by putting the entire equation on the left of the =, and came up with x^2 -7x +1 = 0. But with this equation, I cannot factor it out. Please help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you cannot factor the equation (which happens a lot) you can use the quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%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=%28-7%29%5E2-4%2A1%2A1=45.

Discriminant d=45 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+45+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+45+%29%29%2F2%5C1+=+6.85410196624968
x%5B2%5D+=+%28-%28-7%29-sqrt%28+45+%29%29%2F2%5C1+=+0.145898033750315

Quadratic expression 1x%5E2%2B-7x%2B1 can be factored:
1x%5E2%2B-7x%2B1+=+1%28x-6.85410196624968%29%2A%28x-0.145898033750315%29
Again, the answer is: 6.85410196624968, 0.145898033750315. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B1+%29


So our answer is:
x=0.145898033750315 or x=6.85410196624968