Algebra Examples

x^{2} - 5 x = 24

$x^{2} - 5 x = 24$

Step 1

Subtract

24

$24$ from both sides of the equation.

x^{2} - 5 x - 24 = 0

$x^{2} - 5 x - 24 = 0$

Step 2

Factor

x^{2} - 5 x - 24

$x^{2} - 5 x - 24$ using the AC method.

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Step 2.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 24

$- 24$ and whose sum is

- 5

$- 5$ .

- 8, 3

$- 8, 3$

Step 2.2

Write the factored form using these integers.

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

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

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

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

Step 3

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x - 8 = 0

$x - 8 = 0$

x + 3 = 0

$x + 3 = 0$

Step 4

Set

x - 8

$x - 8$ equal to

0

$0$ and solve for

x

$x$ .

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Step 4.1

Set

x - 8

$x - 8$ equal to

0

$0$ .

x - 8 = 0

$x - 8 = 0$

Step 4.2

Add

8

$8$ to both sides of the equation.

x = 8

$x = 8$

x = 8

$x = 8$

Step 5

Set

x + 3

$x + 3$ equal to

0

$0$ and solve for

x

$x$ .

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Step 5.1

Set

x + 3

$x + 3$ equal to

0

$0$ .

x + 3 = 0

$x + 3 = 0$

Step 5.2

Subtract

3

$3$ from both sides of the equation.

x = - 3

$x = - 3$

x = - 3

$x = - 3$

Step 6

The final solution is all the values that make

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

$(x - 8) (x + 3) = 0$ true.

x = 8, - 3

$x = 8, - 3$