Pre-Algebra Examples

$66 = 3 x^{2} - 24 x + 87$

Step 1

Rewrite the equation as $3 x^{2} - 24 x + 87 = 66$ .

$3 x^{2} - 24 x + 87 = 66$

Step 2

Subtract $66$ from both sides of the equation.

$3 x^{2} - 24 x + 87 - 66 = 0$

Step 3

Subtract $66$ from $87$ .

$3 x^{2} - 24 x + 21 = 0$

Step 4

Factor the left side of the equation.

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Step 4.1

Factor $3$ out of $3 x^{2} - 24 x + 21$ .

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Step 4.1.1

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) - 24 x + 21 = 0$

Step 4.1.2

Factor $3$ out of $- 24 x$ .

$3 (x^{2}) + 3 (- 8 x) + 21 = 0$

Step 4.1.3

Factor $3$ out of $21$ .

$3 x^{2} + 3 (- 8 x) + 3 \cdot 7 = 0$

Step 4.1.4

Factor $3$ out of $3 x^{2} + 3 (- 8 x)$ .

$3 (x^{2} - 8 x) + 3 \cdot 7 = 0$

Step 4.1.5

Factor $3$ out of $3 (x^{2} - 8 x) + 3 \cdot 7$ .

$3 (x^{2} - 8 x + 7) = 0$

Step 4.2

Factor.

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Step 4.2.1

Factor $x^{2} - 8 x + 7$ using the AC method.

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Step 4.2.1.1

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 $7$ and whose sum is $- 8$ .

$- 7, - 1$

Step 4.2.1.2

Write the factored form using these integers.

$3 ((x - 7) (x - 1)) = 0$

Step 4.2.2

Remove unnecessary parentheses.

$3 (x - 7) (x - 1) = 0$

Step 5

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

$x - 7 = 0$

$x - 1 = 0$

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 $x - 1$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 7.2

Add $1$ to both sides of the equation.

$x = 1$

Step 8

The final solution is all the values that make $3 (x - 7) (x - 1) = 0$ true.

$x = 7, 1$