Pre-Algebra Examples

$x^{2} - 9 = (x + 3)$

Step 1

Subtract $x$ from both sides of the equation.

$x^{2} - 9 - x = 3$

Step 2

Subtract $3$ from both sides of the equation.

$x^{2} - 9 - x - 3 = 0$

Step 3

Subtract $3$ from $- 9$ .

$x^{2} - x - 12 = 0$

Step 4

Factor $x^{2} - x - 12$ using the AC method.

Tap for more steps...

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 $- 12$ and whose sum is $- 1$ .

$- 4, 3$

Step 4.2

Write the factored form using these integers.

$(x - 4) (x + 3) = 0$

Step 5

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

$x - 4 = 0$

$x + 3 = 0$

Step 6

Set $x - 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 6.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 6.2

Add $4$ to both sides of the equation.

$x = 4$

Step 7

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

Tap for more steps...

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 $(x - 4) (x + 3) = 0$ true.

$x = 4, - 3$