Algebra Examples

$x^{2} - 8 x + 15 = 0$

Step 1

Factor

$x^{2} - 8 x + 15$ using the AC method.

Tap for more steps...

Step 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

$15$ and whose sum is

$- 8$ .

$- 5, - 3$

Step 1.2

Write the factored form using these integers.

$(x - 5) (x - 3) = 0$

Step 2

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

$0$ , the entire expression will be equal to

$0$ .

$x - 5 = 0$

$x - 3 = 0$

Step 3

Set

$x - 5$ equal to

$0$ and solve for

$x$ .

Tap for more steps...

Step 3.1

Set

$x - 5$ equal to

$0$ .

$x - 5 = 0$

Step 3.2

Add

$5$ to both sides of the equation.

$x = 5$

Step 4

Set

$x - 3$ equal to

$0$ and solve for

$x$ .

Tap for more steps...

Step 4.1

Set

$x - 3$ equal to

$0$ .

$x - 3 = 0$

Step 4.2

Add

$3$ to both sides of the equation.

$x = 3$

Step 5

The final solution is all the values that make

$(x - 5) (x - 3) = 0$ true.

$x = 5, 3$