Pre-Algebra Examples

$36 = \frac{x^{2} - x}{2}$

Step 1

Rewrite the equation as $\frac{x^{2} - x}{2} = 36$ .

$\frac{x^{2} - x}{2} = 36$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{x^{2} - x}{2} = 2 \cdot 36$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{x^{2} - x}{2} = 2 \cdot 36$

Step 3.1.1.2

Rewrite the expression.

$x^{2} - x = 2 \cdot 36$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $36$ .

$x^{2} - x = 72$

Step 4

Subtract $72$ from both sides of the equation.

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

Step 5

Factor $x^{2} - x - 72$ 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 $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Step 5.2

Write the factored form using these integers.

$(x - 9) (x + 8) = 0$

Step 6

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

$x - 9 = 0$

$x + 8 = 0$

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

Add $9$ to both sides of the equation.

$x = 9$

Step 8

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

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Step 8.1

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

$x + 8 = 0$

Step 8.2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 9

The final solution is all the values that make $(x - 9) (x + 8) = 0$ true.

$x = 9, - 8$