Algebra Examples

$(x + 9) (x - 5) = {(x + 1)}^{2}$

Step 1

Simplify $(x + 9) (x - 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + (x + 9) (x - 5) = {(x + 1)}^{2}$

Step 1.2

Simplify by adding zeros.

$(x + 9) (x - 5) = {(x + 1)}^{2}$

Step 1.3

Expand $(x + 9) (x - 5)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x (x - 5) + 9 (x - 5) = {(x + 1)}^{2}$

Step 1.3.2

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 9 (x - 5) = {(x + 1)}^{2}$

Step 1.3.3

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 9 x + 9 \cdot - 5 = {(x + 1)}^{2}$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 + 9 x + 9 \cdot - 5 = {(x + 1)}^{2}$

Step 1.4.1.2

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x + 9 x + 9 \cdot - 5 = {(x + 1)}^{2}$

Step 1.4.1.3

Multiply $9$ by $- 5$ .

$x^{2} - 5 x + 9 x - 45 = {(x + 1)}^{2}$

Step 1.4.2

Add $- 5 x$ and $9 x$ .

$x^{2} + 4 x - 45 = {(x + 1)}^{2}$

Step 2

Simplify ${(x + 1)}^{2}$ .

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Step 2.1

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$x^{2} + 4 x - 45 = (x + 1) (x + 1)$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$x^{2} + 4 x - 45 = x (x + 1) + 1 (x + 1)$

Step 2.2.2

Apply the distributive property.

$x^{2} + 4 x - 45 = x \cdot x + x \cdot 1 + 1 (x + 1)$

Step 2.2.3

Apply the distributive property.

$x^{2} + 4 x - 45 = x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$x^{2} + 4 x - 45 = x^{2} + x \cdot 1 + 1 x + 1 \cdot 1$

Step 2.3.1.2

Multiply $x$ by $1$ .

$x^{2} + 4 x - 45 = x^{2} + x + 1 x + 1 \cdot 1$

Step 2.3.1.3

Multiply $x$ by $1$ .

$x^{2} + 4 x - 45 = x^{2} + x + x + 1 \cdot 1$

Step 2.3.1.4

Multiply $1$ by $1$ .

$x^{2} + 4 x - 45 = x^{2} + x + x + 1$

Step 2.3.2

Add $x$ and $x$ .

$x^{2} + 4 x - 45 = x^{2} + 2 x + 1$

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.

$x^{2} + 4 x - 45 - x^{2} = 2 x + 1$

Step 3.2

Subtract $2 x$ from both sides of the equation.

$x^{2} + 4 x - 45 - x^{2} - 2 x = 1$

Step 3.3

Combine the opposite terms in $x^{2} + 4 x - 45 - x^{2} - 2 x$ .

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Step 3.3.1

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

$4 x - 45 + 0 - 2 x = 1$

Step 3.3.2

Add $4 x - 45$ and $0$ .

$4 x - 45 - 2 x = 1$

Step 3.4

Subtract $2 x$ from $4 x$ .

$2 x - 45 = 1$

Step 4

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

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Step 4.1

Add $45$ to both sides of the equation.

$2 x = 1 + 45$

Step 4.2

Add $1$ and $45$ .

$2 x = 46$

Step 5

Divide each term in $2 x = 46$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 46$ by $2$ .

$\frac{2 x}{2} = \frac{46}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{46}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{46}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $46$ by $2$ .

$x = 23$