Finite Math Examples

$2 a^{2} + 5 a - 12 = a + 4$

Step 1

Move all terms containing $a$ to the left side of the equation.

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Step 1.1

Subtract $a$ from both sides of the equation.

$2 a^{2} + 5 a - 12 - a = 4$

Step 1.2

Subtract $a$ from $5 a$ .

$2 a^{2} + 4 a - 12 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$2 a^{2} + 4 a - 12 - 4 = 0$

Step 3

Subtract $4$ from $- 12$ .

$2 a^{2} + 4 a - 16 = 0$

Step 4

Factor the left side of the equation.

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Step 4.1

Factor $2$ out of $2 a^{2} + 4 a - 16$ .

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Step 4.1.1

Factor $2$ out of $2 a^{2}$ .

$2 (a^{2}) + 4 a - 16 = 0$

Step 4.1.2

Factor $2$ out of $4 a$ .

$2 (a^{2}) + 2 (2 a) - 16 = 0$

Step 4.1.3

Factor $2$ out of $- 16$ .

$2 a^{2} + 2 (2 a) + 2 \cdot - 8 = 0$

Step 4.1.4

Factor $2$ out of $2 a^{2} + 2 (2 a)$ .

$2 (a^{2} + 2 a) + 2 \cdot - 8 = 0$

Step 4.1.5

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

$2 (a^{2} + 2 a - 8) = 0$

Step 4.2

Factor.

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Step 4.2.1

Factor $a^{2} + 2 a - 8$ 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 $- 8$ and whose sum is $2$ .

$- 2, 4$

Step 4.2.1.2

Write the factored form using these integers.

$2 ((a - 2) (a + 4)) = 0$

Step 4.2.2

Remove unnecessary parentheses.

$2 (a - 2) (a + 4) = 0$

Step 5

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

$a - 2 = 0$

$a + 4 = 0$

Step 6

Set $a - 2$ equal to $0$ and solve for $a$ .

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Step 6.1

Set $a - 2$ equal to $0$ .

$a - 2 = 0$

Step 6.2

Add $2$ to both sides of the equation.

$a = 2$

Step 7

Set $a + 4$ equal to $0$ and solve for $a$ .

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Step 7.1

Set $a + 4$ equal to $0$ .

$a + 4 = 0$

Step 7.2

Subtract $4$ from both sides of the equation.

$a = - 4$

Step 8

The final solution is all the values that make $2 (a - 2) (a + 4) = 0$ true.

$a = 2, - 4$

Step 9