Solve the Quadratic Equation: 4x² - 4x + 1 = 0

Solve the following equation:

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

To solve the equation $4x^2 - 4x + 1 = 0$, we will use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

First, we identify $a = 4$, $b = -4$, and $c = 1$.

Calculate the discriminant:

$b^2 - 4ac = (-4)^2 - 4 \times 4 \times 1 = 16 - 16 = 0$

Since the discriminant is 0, there is one real repeated root.

Substitute into the quadratic formula:

$x = \frac{-(-4) \pm \sqrt{0}}{2 \times 4} = \frac{4}{8} = \frac{1}{2}$

Therefore, the solution to the equation is $x = \frac{1}{2}$.