Algebra Examples

x^{2} - 9 x + 8 = 0

$x^{2} - 9 x + 8 = 0$

Step 1

Factor

x^{2} - 9 x + 8

$x^{2} - 9 x + 8$ 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

8

$8$ and whose sum is

- 9

$- 9$ .

- 8, - 1

$- 8, - 1$

Step 1.2

Write the factored form using these integers.

(x - 8) (x - 1) = 0

$(x - 8) (x - 1) = 0$

(x - 8) (x - 1) = 0

$(x - 8) (x - 1) = 0$

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

$0$ .

x - 8 = 0

$x - 8 = 0$

x - 1 = 0

$x - 1 = 0$

Step 3

Set

x - 8

$x - 8$ equal to

0

$0$ and solve for

x

$x$ .

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Step 3.1

Set

x - 8

$x - 8$ equal to

0

$0$ .

x - 8 = 0

$x - 8 = 0$

Step 3.2

Add

8

$8$ to both sides of the equation.

x = 8

$x = 8$

x = 8

$x = 8$

Step 4

Set

x - 1

$x - 1$ equal to

0

$0$ and solve for

x

$x$ .

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Step 4.1

Set

x - 1

$x - 1$ equal to

0

$0$ .

x - 1 = 0

$x - 1 = 0$

Step 4.2

Add

1

$1$ to both sides of the equation.

x = 1

$x = 1$

x = 1

$x = 1$

Step 5

The final solution is all the values that make

(x - 8) (x - 1) = 0

$(x - 8) (x - 1) = 0$ true.

x = 8, 1

$x = 8, 1$

x^{2} - 9 x + 8 = 0

$x^{2} - 9 x + 8 = 0$

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