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

Question 58913: Solve:
4x^2+1=2x
Found 2 solutions by aaaaaaaa, checkley71:
Answer by aaaaaaaa(138) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is

Here's your graph:

Answer by checkley71(8403) (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

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