SOLUTION: I need help solving this problem, please show me how you work this problem out... Thank you Happy Thanksgiving Solve equation using the quadratic formula 4m^2 - 8m + 1 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need help solving this problem, please show me how you work this problem out... Thank you Happy Thanksgiving Solve equation using the quadratic formula 4m^2 - 8m + 1 = 0      Log On


   

Question 169891: I need help solving this problem, please show me how you work this problem out... Thank you Happy Thanksgiving
Solve equation using the quadratic formula
4m^2 - 8m + 1 = 0
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
4m^2 - 8m + 1 = 0
.
To solve,
always try factoring first
failing that, use the quadratic equation.
.
In this case, we must use the quadratic equation.
Doing so will yield:
m = {1.866, 0.134}
.
Details below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation am%5E2%2Bbm%2Bc=0 (in our case 4m%5E2%2B-8m%2B1+=+0) has the following solutons:

m%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=%28-8%29%5E2-4%2A4%2A1=48.

Discriminant d=48 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+48+%29%29%2F2%5Ca.

m%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+48+%29%29%2F2%5C4+=+1.86602540378444
m%5B2%5D+=+%28-%28-8%29-sqrt%28+48+%29%29%2F2%5C4+=+0.133974596215561

Quadratic expression 4m%5E2%2B-8m%2B1 can be factored:
4m%5E2%2B-8m%2B1+=+4%28m-1.86602540378444%29%2A%28m-0.133974596215561%29
Again, the answer is: 1.86602540378444, 0.133974596215561. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-8%2Ax%2B1+%29