Finite Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x - 2)}^{2}$ as $(x - 2) (x - 2)$ .

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

Step 2.1.2

Expand $(x - 2) (x - 2)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

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

Step 2.1.2.2

Apply the distributive property.

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

Step 2.1.2.3

Apply the distributive property.

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

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

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

Step 2.1.3.1.2

Move $- 2$ to the left of $x$ .

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

Step 2.1.3.1.3

Multiply $- 2$ by $- 2$ .

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

Step 2.1.3.2

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

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

Step 2.1.4

Apply the distributive property.

$x^{2} - 4 x + 4 - x^{2} - (- 4 x) - 1 \cdot 4 = 0$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $- 4$ by $- 1$ .

$x^{2} - 4 x + 4 - x^{2} + 4 x - 1 \cdot 4 = 0$

Step 2.1.5.2

Multiply $- 1$ by $4$ .

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

Step 2.2

Combine the opposite terms in $x^{2} - 4 x + 4 - x^{2} + 4 x - 4$ .

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Step 2.2.1

Subtract $x^{2}$ from $x^{2}$ .

$- 4 x + 4 + 0 + 4 x - 4 = 0$

Step 2.2.2

Add $- 4 x + 4$ and $0$ .

$- 4 x + 4 + 4 x - 4 = 0$

Step 2.2.3

Add $- 4 x$ and $4 x$ .

$0 + 4 - 4 = 0$

Step 2.2.4

Add $0$ and $4$ .

$4 - 4 = 0$

Step 2.2.5

Subtract $4$ from $4$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true