Finite Math Examples

$(x - 1) (x + 7) = 20$

Step 1

Simplify $(x - 1) (x + 7)$ .

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Step 1.1

Expand $(x - 1) (x + 7)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$x (x + 7) - 1 (x + 7) = 20$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 7 - 1 (x + 7) = 20$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 7 - 1 x - 1 \cdot 7 = 20$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 7 - 1 x - 1 \cdot 7 = 20$

Step 1.2.1.2

Move $7$ to the left of $x$ .

$x^{2} + 7 \cdot x - 1 x - 1 \cdot 7 = 20$

Step 1.2.1.3

Rewrite $- 1 x$ as $- x$ .

$x^{2} + 7 x - x - 1 \cdot 7 = 20$

Step 1.2.1.4

Multiply $- 1$ by $7$ .

$x^{2} + 7 x - x - 7 = 20$

Step 1.2.2

Subtract $x$ from $7 x$ .

$x^{2} + 6 x - 7 = 20$

Step 2

Subtract $20$ from both sides of the equation.

$x^{2} + 6 x - 7 - 20 = 0$

Step 3

Subtract $20$ from $- 7$ .

$x^{2} + 6 x - 27 = 0$

Step 4

Factor $x^{2} + 6 x - 27$ using the AC method.

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Step 4.1

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 $- 27$ and whose sum is $6$ .

$- 3, 9$

Step 4.2

Write the factored form using these integers.

$(x - 3) (x + 9) = 0$

Step 5

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

$x - 3 = 0$

$x + 9 = 0$

Step 6

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

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Step 6.1

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

$x - 3 = 0$

Step 6.2

Add $3$ to both sides of the equation.

$x = 3$

Step 7

Set $x + 9$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Step 7.2

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 8

The final solution is all the values that make $(x - 3) (x + 9) = 0$ true.

$x = 3, - 9$