Finite Math Examples

$2 x + x^{2} = 24$

Step 1

Subtract $24$ from both sides of the equation.

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

Step 2

Factor the left side of the equation.

Tap for more steps...

Step 2.1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$2 u + u^{2} - 24 = 0$

Step 2.2

Factor $2 u + u^{2} - 24$ using the AC method.

Tap for more steps...

Step 2.2.1

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 $2$ .

$- 4, 6$

Step 2.2.2

Write the factored form using these integers.

$(u - 4) (u + 6) = 0$

Step 2.3

Replace all occurrences of $u$ with $x$ .

$(x - 4) (x + 6) = 0$

Step 3

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

$x - 4 = 0$

$x + 6 = 0$

Step 4

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

Tap for more steps...

Step 4.1

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

$x - 4 = 0$

Step 4.2

Add $4$ to both sides of the equation.

$x = 4$

Step 5

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

Tap for more steps...

Step 5.1

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

$x + 6 = 0$

Step 5.2

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 6

The final solution is all the values that make $(x - 4) (x + 6) = 0$ true.

$x = 4, - 6$