Finite Math Examples

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

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

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

4 x = 2 \cdot x \cdot 2

$4 x = 2 \cdot x \cdot 2$

Step 1.3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 2 + 2^{2} = 0

$x^{2} + 2 \cdot x \cdot 2 + 2^{2} = 0$

Step 1.4

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

a = x

$a = x$ and

b = 2

$b = 2$ .

{(x + 2)}^{2} = 0

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

{(x + 2)}^{2} = 0

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

Step 2

Set the

x + 2

$x + 2$ equal to

0

$0$ .

x + 2 = 0

$x + 2 = 0$

Step 3

Subtract

2

$2$ from both sides of the equation.

x = - 2

$x = - 2$

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