Basic Math Examples

a^{2} - 10 a + 24 = 0

$a^{2} - 10 a + 24 = 0$

Step 1

Factor

a^{2} - 10 a + 24

$a^{2} - 10 a + 24$ using the AC method.

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Step 1.1

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

- 10

$- 10$ .

- 6, - 4

$- 6, - 4$

Step 1.2

Write the factored form using these integers.

(a - 6) (a - 4) = 0

$(a - 6) (a - 4) = 0$

(a - 6) (a - 4) = 0

$(a - 6) (a - 4) = 0$

Step 2

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

0

$0$ , the entire expression will be equal to

0

$0$ .

a - 6 = 0

$a - 6 = 0$

a - 4 = 0

$a - 4 = 0$

Step 3

Set

a - 6

$a - 6$ equal to

0

$0$ and solve for

a

$a$ .

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Step 3.1

Set

a - 6

$a - 6$ equal to

0

$0$ .

a - 6 = 0

$a - 6 = 0$

Step 3.2

Add

6

$6$ to both sides of the equation.

a = 6

$a = 6$

a = 6

$a = 6$

Step 4

Set

a - 4

$a - 4$ equal to

0

$0$ and solve for

a

$a$ .

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Step 4.1

Set

a - 4

$a - 4$ equal to

0

$0$ .

a - 4 = 0

$a - 4 = 0$

Step 4.2

Add

4

$4$ to both sides of the equation.

a = 4

$a = 4$

a = 4

$a = 4$

Step 5

The final solution is all the values that make

(a - 6) (a - 4) = 0

$(a - 6) (a - 4) = 0$ true.

a = 6, 4

$a = 6, 4$