Algebra Examples

$5 + x^{2} = (x + 1) (x + 6)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(x + 1) (x + 6) = 5 + x^{2}$

Step 2

Simplify $(x + 1) (x + 6)$ .

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Step 2.1

Rewrite.

$0 + 0 + (x + 1) (x + 6) = 5 + x^{2}$

Step 2.2

Simplify by adding zeros.

$(x + 1) (x + 6) = 5 + x^{2}$

Step 2.3

Expand $(x + 1) (x + 6)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$x (x + 6) + 1 (x + 6) = 5 + x^{2}$

Step 2.3.2

Apply the distributive property.

$x \cdot x + x \cdot 6 + 1 (x + 6) = 5 + x^{2}$

Step 2.3.3

Apply the distributive property.

$x \cdot x + x \cdot 6 + 1 x + 1 \cdot 6 = 5 + x^{2}$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 6 + 1 x + 1 \cdot 6 = 5 + x^{2}$

Step 2.4.1.2

Move $6$ to the left of $x$ .

$x^{2} + 6 \cdot x + 1 x + 1 \cdot 6 = 5 + x^{2}$

Step 2.4.1.3

Multiply $x$ by $1$ .

$x^{2} + 6 x + x + 1 \cdot 6 = 5 + x^{2}$

Step 2.4.1.4

Multiply $6$ by $1$ .

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

Step 2.4.2

Add $6 x$ and $x$ .

$x^{2} + 7 x + 6 = 5 + x^{2}$

Step 3

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

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Step 3.1

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

$x^{2} + 7 x + 6 - x^{2} = 5$

Step 3.2

Combine the opposite terms in $x^{2} + 7 x + 6 - x^{2}$ .

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Step 3.2.1

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

$7 x + 6 + 0 = 5$

Step 3.2.2

Add $7 x + 6$ and $0$ .

$7 x + 6 = 5$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Subtract $6$ from both sides of the equation.

$7 x = 5 - 6$

Step 4.2

Subtract $6$ from $5$ .

$7 x = - 1$

Step 5

Divide each term in $7 x = - 1$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 x = - 1$ by $7$ .

$\frac{7 x}{7} = \frac{- 1}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 1}{7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{7}$

Decimal Form:

$x = - 0.\overline{142857}$