Finite Math Examples

$(x) (x + 2) = 5 (x + 1) + 13$

Step 1

Simplify $x (x + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + x (x + 2) = 5 (x + 1) + 13$

Step 1.2

Simplify by adding zeros.

$x (x + 2) = 5 (x + 1) + 13$

Step 1.3

Apply the distributive property.

$x \cdot x + x \cdot 2 = 5 (x + 1) + 13$

Step 1.4

Simplify the expression.

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Step 1.4.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 = 5 (x + 1) + 13$

Step 1.4.2

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

$x^{2} + 2 x = 5 (x + 1) + 13$

Step 2

Simplify $5 (x + 1) + 13$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x^{2} + 2 x = 5 x + 5 \cdot 1 + 13$

Step 2.1.2

Multiply $5$ by $1$ .

$x^{2} + 2 x = 5 x + 5 + 13$

Step 2.2

Add $5$ and $13$ .

$x^{2} + 2 x = 5 x + 18$

Step 3

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

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Step 3.1

Subtract $5 x$ from both sides of the equation.

$x^{2} + 2 x - 5 x = 18$

Step 3.2

Subtract $5 x$ from $2 x$ .

$x^{2} - 3 x = 18$

Step 4

Subtract $18$ from both sides of the equation.

$x^{2} - 3 x - 18 = 0$

Step 5

Factor $x^{2} - 3 x - 18$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $- 3$ .

$- 6, 3$

Step 5.2

Write the factored form using these integers.

$(x - 6) (x + 3) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 6 = 0$

$x + 3 = 0$

Step 7

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 7.2

Add $6$ to both sides of the equation.

$x = 6$

Step 8

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 8.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 9

The final solution is all the values that make $(x - 6) (x + 3) = 0$ true.

$x = 6, - 3$