Solve by Factoring 0=x^2-4x+4

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

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

Add $4 x$ to both sides of the equation.

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

Subtract $4$ from both sides of the equation.

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

Step 2

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 1 \cdot - 4 = 4$ and whose sum is $b = 4$ .

Factor $4$ out of $4 x$ .

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

Rewrite $4$ as $2$ plus $2$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$x (- x + 2) - 2 (- x + 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $- x + 2$ .

$(- x + 2) (x - 2) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$- x + 2 = 0$

$x - 2 = 0$

Step 4

Set $- x + 2$ equal to $0$ and solve for $x$ .

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

$- x + 2 = 0$

Solve $- x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

Step 5

The final solution is all the values that make $(- x + 2) (x - 2) = 0$ true.

$x = 2$

Solve by Factoring 0=x^2-4x+4

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