SOLUTION: Solve: 4x^2+1=2x

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Question 58913: Solve:
4x^2+1=2x

Found 2 solutions by aaaaaaaa, checkley71:
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B1=2x
4x%5E2-2x%2B1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-2x%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=%28-2%29%5E2-4%2A4%2A1=-12.

The discriminant -12 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -12 is + or - sqrt%28+12%29+=+3.46410161513775.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-2%2Ax%2B1+%29

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
4X^2+1=2X
4X^2-2X+1=0 USING THE QUADRATIC EQUATION X=(-B+-SQRT[B^2-4AC])/2A WE GET
X=(2+-SQRT[4-4*4*1])/8
X=(2+-SQRT[4-16])/8
X=(2+-SQRT[-12])/8
X=(2+-3.464i)/8
X=2/8+3.464i/8
X=.25+.433i
AND
X=2/8-3.464i/8
X=.25-.433i