x^{2}-4x+4=0   what is the correct procedimineto  using the quadratic formula 

To solve the quadratic equation \( x^2 - 4x + 4 = 0 \) using the quadratic formula, follow these steps:

### Step 1: Identify the coefficients
In the quadratic equation \( ax^2 + bx + c = 0 \), identify the values of \( a \), \( b \), and \( c \).

For \( x^2 - 4x + 4 = 0 \):
- \( a = 1 \)
- \( b = -4 \)
- \( c = 4 \)

### Step 2: Write the quadratic formula
The quadratic formula is given by:

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

### Step 3: Substitute the values of \( a \), \( b \), and \( c \)

Substitute \( a = 1 \), \( b = -4 \), and \( c = 4 \) into the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(4)}}{2(1)}
\]

### Step 4: Simplify inside the square root

First, calculate \( b^2 - 4ac \):

\[
(-4)^2 - 4(1)(4) = 16 - 16 = 0
\]

So the expression simplifies to:

\[
x = \frac{4 \pm \sqrt{0}}{2}
\]

### Step 5: Simplify further

Since \( \sqrt{0} = 0 \), the quadratic formula becomes:

\[
x = \frac{4 \pm 0}{2}
\]

\[
x = \frac{4}{2}
\]

\[
x = 2
\]

### Step 6: Final solution
There is only one solution: \( x = 2 \).

This quadratic equation has a **double root**, meaning the solution \( x = 2 \) has multiplicity 2.

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Would you like more details, or do you have any questions?

### 5 Related Questions:
1. How do you recognize when a quadratic equation has a double root?
2. How do you factor a quadratic equation like this without using the quadratic formula?
3. What are the conditions for a quadratic equation to have real, distinct roots?
4. How does the discriminant \( b^2 - 4ac \) affect the nature of the solutions?
5. How would the solution change if the constant term were different?

### Tip:
The discriminant (\( b^2 - 4ac \)) determines the type of roots a quadratic equation will have: if it's zero, there's one real double root; if positive, two distinct real roots; and if negative, two complex roots.

x^{2}-4x+4=0   what is the correct procedimineto  using the quadratic formula

Learn the step-by-step process to solve the quadratic equation x^2 - 4x + 4 using the quadratic formula. This guide covers algebraic concepts, including identifying coefficients, calculating the discriminant, and finding the double root solution. Suitable for students in Grades 8-10.

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