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

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

Step 1

Simplify the equation into a proper form to complete the square.

Subtract $4$ from both sides of the equation.

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

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

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

Subtract $2 x$ from $- 4 x$ .

$x^{2} - 6 x = - 4$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 3)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 6 x + {(- 3)}^{2} = - 4 + {(- 3)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 3$ to the power of $2$ .

$x^{2} - 6 x + 9 = - 4 + {(- 3)}^{2}$

Simplify the right side.

Simplify $- 4 + {(- 3)}^{2}$ .

Raise $- 3$ to the power of $2$ .

$x^{2} - 6 x + 9 = - 4 + 9$

Add $- 4$ and $9$ .

$x^{2} - 6 x + 9 = 5$

Step 5

Factor the perfect trinomial square into ${(x - 3)}^{2}$ .

${(x - 3)}^{2} = 5$

Step 6

Solve the equation for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 3 = \pm \sqrt{5}$

Add $3$ to both sides of the equation.

$x = \pm \sqrt{5} + 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{5} + 3$

Decimal Form:

$x = 5.23606797 \dots, 0.76393202 \dots$