SOLUTION: Solve the question by completing the square. 4x^2-5x+1=0. I keep messing the answer up. The answer should be x=1 and x=1/4

Algebra ->  Square-cubic-other-roots -> SOLUTION: Solve the question by completing the square. 4x^2-5x+1=0. I keep messing the answer up. The answer should be x=1 and x=1/4      Log On


   

Question 861281: Solve the question by completing the square. 4x^2-5x+1=0. I keep messing the answer up. The answer should be x=1 and x=1/4
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
by factoring
4x^2-5x+1=0
(4x-1)*(x-1)
complete the square
4x^2-5x+1=0
x^2-5/4x=-1/4
take half of 5/4 and square it
5/8^2= 25/64
x^2-5/4x+25/64=-16/64+25/64
(x-5/8)^2=9/64


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%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%2A4%2A1=9.

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

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+9+%29%29%2F2%5C4+=+1
x%5B2%5D+=+%28-%28-5%29-sqrt%28+9+%29%29%2F2%5C4+=+0.25

Quadratic expression 4x%5E2%2B-5x%2B1 can be factored:
4x%5E2%2B-5x%2B1+=+4%28x-1%29%2A%28x-0.25%29
Again, the answer is: 1, 0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-5%2Ax%2B1+%29