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

Question

Solve the following equation:

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

00:06 Let's find the value of X.

00:09 We'll start by using the roots formula.

00:34 First, identify the coefficients from the equation.

00:50 Now, substitute the given values and begin solving.

01:14 Calculate the square and the products carefully.

01:34 Remember, the square root of zero is always zero.

01:39 When the root equals zero, it means there's only one solution.

02:01 And that's how we find the answer to this question.

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 $x = \frac{1}{2}$ .

$x=\frac{1}{2}$