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

Solve the following equation:

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

To solve this problem, we'll follow these steps:

• Step 1: Recognize the given quadratic equation $x^2 - 4x + 4 = 0$ as a perfect square trinomial.
• Step 2: Identify the factored form, which is $(x - 2)^2 = 0$.
• Step 3: Solve the factored equation to find the value of $x$.

Now, let's work through each step:

Step 1: The problem gives us the quadratic equation $x^2 - 4x + 4 = 0$. This equation is a perfect square trinomial because it can be rewritten as $(x - 2)^2 = 0$.

Step 2: Recognize and rewrite the equation in its factored form:

$(x - 2)^2 = 0$.

Step 3: To solve this factored equation, set the factor equal to zero:

$x - 2 = 0$.

Solving for $x$, we get:

$x = 2$.

In this case, the equation has a double root, $x = 2$.

Therefore, the solution to the problem is $x = 2$.