Precalculus Examples

$x^{2} - 4 = 3 x + 14$

Step 1

Subtract $3 x$ from both sides of the equation.

$x^{2} - 4 - 3 x = 14$

Step 2

Subtract $14$ from both sides of the equation.

$x^{2} - 4 - 3 x - 14 = 0$

Step 3

Subtract $14$ from $- 4$ .

$x^{2} - 3 x - 18 = 0$

Step 4

Factor $x^{2} - 3 x - 18$ 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 $- 18$ and whose sum is $- 3$ .

$- 6, 3$

Step 4.2

Write the factored form using these integers.

$(x - 6) (x + 3) = 0$

Step 5

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

$x - 6 = 0$

$x + 3 = 0$

Step 6

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

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Step 6.1

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

$x - 6 = 0$

Step 6.2

Add $6$ to both sides of the equation.

$x = 6$

Step 7

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 7.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 8

The final solution is all the values that make $(x - 6) (x + 3) = 0$ true.

$x = 6, - 3$