Pre-Algebra Examples

$z^{2} + 14 = 9 z$

Step 1

Subtract $9 z$ from both sides of the equation.

$z^{2} + 14 - 9 z = 0$

Step 2

Factor $z^{2} + 14 - 9 z$ using the AC method.

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Step 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 $14$ and whose sum is $- 9$ .

$- 7, - 2$

Step 2.2

Write the factored form using these integers.

$(z - 7) (z - 2) = 0$

Step 3

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

$z - 7 = 0$

$z - 2 = 0$

Step 4

Set $z - 7$ equal to $0$ and solve for $z$ .

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Step 4.1

Set $z - 7$ equal to $0$ .

$z - 7 = 0$

Step 4.2

Add $7$ to both sides of the equation.

$z = 7$

Step 5

Set $z - 2$ equal to $0$ and solve for $z$ .

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Step 5.1

Set $z - 2$ equal to $0$ .

$z - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$z = 2$

Step 6

The final solution is all the values that make $(z - 7) (z - 2) = 0$ true.

$z = 7, 2$