Pre-Algebra Examples

$(x + 2) (x) (2) = 96$

Step 1

Divide each term in $(x + 2) (x) \cdot 2 = 96$ by $2$ and simplify.

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Step 1.1

Divide each term in $(x + 2) (x) \cdot 2 = 96$ by $2$ .

$\frac{(x + 2) (x) \cdot 2}{2} = \frac{96}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{(x + 2) (x) \cdot 2}{2} = \frac{96}{2}$

Step 1.2.1.2

Divide $(x + 2) (x)$ by $1$ .

$(x + 2) (x) = \frac{96}{2}$

Step 1.2.2

Apply the distributive property.

$x \cdot x + 2 x = \frac{96}{2}$

Step 1.2.3

Multiply $x$ by $x$ .

$x^{2} + 2 x = \frac{96}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $96$ by $2$ .

$x^{2} + 2 x = 48$

Step 2

Subtract $48$ from both sides of the equation.

$x^{2} + 2 x - 48 = 0$

Step 3

Factor $x^{2} + 2 x - 48$ using the AC method.

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Step 3.1

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 $- 48$ and whose sum is $2$ .

$- 6, 8$

Step 3.2

Write the factored form using these integers.

$(x - 6) (x + 8) = 0$

Step 4

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

$x - 6 = 0$

$x + 8 = 0$

Step 5

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

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Step 5.1

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

$x - 6 = 0$

Step 5.2

Add $6$ to both sides of the equation.

$x = 6$

Step 6

Set $x + 8$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Step 6.2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 7

The final solution is all the values that make $(x - 6) (x + 8) = 0$ true.

$x = 6, - 8$