Finite Math Examples

$(x + 9) (x - 8) = 38$

Step 1

Simplify $(x + 9) (x - 8)$ .

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Step 1.1

Expand $(x + 9) (x - 8)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$x (x - 8) + 9 (x - 8) = 38$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 8 + 9 (x - 8) = 38$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 8 + 9 x + 9 \cdot - 8 = 38$

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 $x$ .

$x^{2} + x \cdot - 8 + 9 x + 9 \cdot - 8 = 38$

Step 1.2.1.2

Move $- 8$ to the left of $x$ .

$x^{2} - 8 \cdot x + 9 x + 9 \cdot - 8 = 38$

Step 1.2.1.3

Multiply $9$ by $- 8$ .

$x^{2} - 8 x + 9 x - 72 = 38$

Step 1.2.2

Add $- 8 x$ and $9 x$ .

$x^{2} + x - 72 = 38$

Step 2

Subtract $38$ from both sides of the equation.

$x^{2} + x - 72 - 38 = 0$

Step 3

Subtract $38$ from $- 72$ .

$x^{2} + x - 110 = 0$

Step 4

Factor $x^{2} + x - 110$ 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 $- 110$ and whose sum is $1$ .

$- 10, 11$

Step 4.2

Write the factored form using these integers.

$(x - 10) (x + 11) = 0$

Step 5

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

$x - 10 = 0$

$x + 11 = 0$

Step 6

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 6.2

Add $10$ to both sides of the equation.

$x = 10$

Step 7

Set $x + 11$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 11$ equal to $0$ .

$x + 11 = 0$

Step 7.2

Subtract $11$ from both sides of the equation.

$x = - 11$

Step 8

The final solution is all the values that make $(x - 10) (x + 11) = 0$ true.

$x = 10, - 11$