Pre-Algebra Examples

$252 = (x + 2) x \cdot 4$

Step 1

Rewrite the equation as $(x + 2) x \cdot 4 = 252$ .

$(x + 2) x \cdot 4 = 252$

Step 2

Divide each term in $(x + 2) x \cdot 4 = 252$ by $4$ and simplify.

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Step 2.1

Divide each term in $(x + 2) x \cdot 4 = 252$ by $4$ .

$\frac{(x + 2) x \cdot 4}{4} = \frac{252}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{(x + 2) x \cdot 4}{4} = \frac{252}{4}$

Step 2.2.1.2

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

$(x + 2) x = \frac{252}{4}$

Step 2.2.2

Apply the distributive property.

$x \cdot x + 2 x = \frac{252}{4}$

Step 2.2.3

Multiply $x$ by $x$ .

$x^{2} + 2 x = \frac{252}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $252$ by $4$ .

$x^{2} + 2 x = 63$

Step 3

Subtract $63$ from both sides of the equation.

$x^{2} + 2 x - 63 = 0$

Step 4

Factor $x^{2} + 2 x - 63$ 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 $- 63$ and whose sum is $2$ .

$- 7, 9$

Step 4.2

Write the factored form using these integers.

$(x - 7) (x + 9) = 0$

Step 5

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

$x - 7 = 0$

$x + 9 = 0$

Step 6

Set $x - 7$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 6.2

Add $7$ to both sides of the equation.

$x = 7$

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 $(x - 7) (x + 9) = 0$ true.

$x = 7, - 9$