Solve by Completing the Square x^2-4x+4=0

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

Step 1

Subtract $4$ from both sides of the equation.

$x^{2} - 4 x = - 4$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 2)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 4 x + {(- 2)}^{2} = - 4 + {(- 2)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 2$ to the power of $2$ .

$x^{2} - 4 x + 4 = - 4 + {(- 2)}^{2}$

Simplify the right side.

Simplify $- 4 + {(- 2)}^{2}$ .

Raise $- 2$ to the power of $2$ .

$x^{2} - 4 x + 4 = - 4 + 4$

Add $- 4$ and $4$ .

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

Step 5

Factor the perfect trinomial square into ${(x - 2)}^{2}$ .

${(x - 2)}^{2} = 0$

Step 6

Solve the equation for $x$ .

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$