Algebra Examples

y = x^{2} + 2 x + 1

$y = x^{2} + 2 x + 1$

Step 1

Set

x^{2} + 2 x + 1

$x^{2} + 2 x + 1$ equal to

0

$0$ .

x^{2} + 2 x + 1 = 0

$x^{2} + 2 x + 1 = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Factor using the perfect square rule.

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Step 2.1.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

x^{2} + 2 x + 1^{2} = 0

$x^{2} + 2 x + 1^{2} = 0$

Step 2.1.2

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

2 x = 2 \cdot x \cdot 1

$2 x = 2 \cdot x \cdot 1$

Step 2.1.3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 1 + 1^{2} = 0

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

Step 2.1.4

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 = 1

$b = 1$ .

{(x + 1)}^{2} = 0

${(x + 1)}^{2} = 0$

{(x + 1)}^{2} = 0

${(x + 1)}^{2} = 0$

Step 2.2

Set the

x + 1

$x + 1$ equal to

0

$0$ .

x + 1 = 0

$x + 1 = 0$

Step 2.3

Subtract

1

$1$ from both sides of the equation.

x = - 1

$x = - 1$ (Multiplicity of

2

$2$ )

x = - 1

$x = - 1$ (Multiplicity of

2

$2$ )

Step 3

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