Move all terms not containing `x` to the right-hand side of the
equation.

`4x^2-4x = -1`

To set the left-hand side of the equation equal to `0` , move all
the expressions to the left-hand side.

`4x^2-4x+1=0`

Remove the fraction by multiplying the first term of the
factor by the denominator of the second term.

`(2x-1)(2x-1)=0`

Set each of the factors of the left-hand side of the
equation equal to `0` .

`2x-1=0`

Since `-1` does not contain the variable to solve for, move it to the
right-hand side of the equation by adding `1` to both sides.

`2x=1`

Divide each term in the equation by `2` .

`x=1/2`

Factor: `4x^2 = 4 x-1`

`4x^2-4x + 1 = 0`

`(2x - 1)(2x-1) = 0`

The root is x = `1/2.`

The equation 4x^2 = 4x - 1 has to be solved for x.

Write the equation in the standard form of a quadratic equation ax^2 + bx + c = 0

4x^2 = 4x - 1

=> 4x^2 - 4x + 1 = 0

The polynomial 4x^2 - 4x + 1 has to be factored and each of them equated to 0 to determine the root.

4x^2 - 4x + 1 = 0

Notice that 4x^2 = (2x)^2 and 4x = 2*2x*1. Substituting the same gives: (2x)^2 - 2*2x*1 + 1^2 = 0

The left hand side is in the form a^2 - 2*a*b + b^2 which is equal to (a - b)^2

4x^2 - 4x + 1 = 0

=> (2x - 1)^2 = 0

=> x = 1/2

**The solution of the equation 4x^2 = 4x - 1 is x = 1/2**

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