Solve $\color{blue}{-x^2+4x-4 = 0}$ using factoring.

$$ \color{blue}{ x = 2 }$$

First we need to factor trinomial $ \color{blue}{ -x^2+4x-4 } $ and than we use factored form to solve an equation $ \color{blue}{ -x^2+4x-4 = 0} $.

**Step 1:** We can simplify equation by multiplying both sides by **-1**.
After multiplying we have the following equation:

** Step 2:**

Both the first and third terms are perfect squares.

$$ x^2 = \left( \color{blue}{ x } \right)^2 ~~ \text{and} ~~ 4 = \left( \color{red}{ 2 } \right)^2 $$The middle term ( $ -4x $ ) is two times the product of the terms that are squared.

$$ -4x = - 2 \cdot \color{blue}{x} \cdot \color{red}{2} $$We can conclude that the polynomial $ x^{2}-4x+4 $ is a **perfect square trinomial**, so we will use the formula below.

In this example we have $ \color{blue}{ A = x } $ and $ \color{red}{ B = 2 } $ so,

$$ x^{2}-4x+4 = ( \color{blue}{ x } - \color{red}{ 2 } )^2 $$** Step 3:** Set each factor to zero and solve equations.

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