Pre-Algebra Examples

$- x^{2} - 10 x - 21 = x^{2} + 12 x + 27$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $x^{2}$ from both sides of the equation.

$- x^{2} - 10 x - 21 - x^{2} = 12 x + 27$

Step 1.2

Subtract $12 x$ from both sides of the equation.

$- x^{2} - 10 x - 21 - x^{2} - 12 x = 27$

Step 1.3

Subtract $x^{2}$ from $- x^{2}$ .

$- 2 x^{2} - 10 x - 21 - 12 x = 27$

Step 1.4

Subtract $12 x$ from $- 10 x$ .

$- 2 x^{2} - 22 x - 21 = 27$

Step 2

Subtract $27$ from both sides of the equation.

$- 2 x^{2} - 22 x - 21 - 27 = 0$

Step 3

Subtract $27$ from $- 21$ .

$- 2 x^{2} - 22 x - 48 = 0$

Step 4

Factor the left side of the equation.

Tap for more steps...

Step 4.1

Factor $- 2$ out of $- 2 x^{2} - 22 x - 48$ .

Tap for more steps...

Step 4.1.1

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

$- 2 x^{2} - 22 x - 48 = 0$

Step 4.1.2

Factor $- 2$ out of $- 22 x$ .

$- 2 x^{2} - 2 (11 x) - 48 = 0$

Step 4.1.3

Factor $- 2$ out of $- 48$ .

$- 2 x^{2} - 2 (11 x) - 2 \cdot 24 = 0$

Step 4.1.4

Factor $- 2$ out of $- 2 (x^{2}) - 2 (11 x)$ .

$- 2 (x^{2} + 11 x) - 2 \cdot 24 = 0$

Step 4.1.5

Factor $- 2$ out of $- 2 (x^{2} + 11 x) - 2 (24)$ .

$- 2 (x^{2} + 11 x + 24) = 0$

Step 4.2

Factor.

Tap for more steps...

Step 4.2.1

Factor $x^{2} + 11 x + 24$ using the AC method.

Tap for more steps...

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 $24$ and whose sum is $11$ .

$3, 8$

Step 4.2.1.2

Write the factored form using these integers.

$- 2 ((x + 3) (x + 8)) = 0$

Step 4.2.2

Remove unnecessary parentheses.

$- 2 (x + 3) (x + 8) = 0$

Step 5

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

$x + 3 = 0$

$x + 8 = 0$

Step 6

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

Tap for more steps...

Step 6.1

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

$x + 3 = 0$

Step 6.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 7

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

Tap for more steps...

Step 7.1

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

$x + 8 = 0$

Step 7.2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 8

The final solution is all the values that make $- 2 (x + 3) (x + 8) = 0$ true.

$x = - 3, - 8$