Solve by Factoring z^2+9=10z

$z^{2} + 9 = 10 z$

Step 1

Subtract $10 z$ from both sides of the equation.

$z^{2} + 9 - 10 z = 0$

Step 2

Factor $z^{2} + 9 - 10 z$ using the AC method.

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 $9$ and whose sum is $- 10$ .

$- 9, - 1$

Write the factored form using these integers.

$(z - 9) (z - 1) = 0$

Step 3

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

$z - 9 = 0$

$z - 1 = 0$

Step 4

Set $z - 9$ equal to $0$ and solve for $z$ .

Set $z - 9$ equal to $0$ .

$z - 9 = 0$

Add $9$ to both sides of the equation.

$z = 9$

Step 5

Set $z - 1$ equal to $0$ and solve for $z$ .

Set $z - 1$ equal to $0$ .

$z - 1 = 0$

Add $1$ to both sides of the equation.

$z = 1$

Step 6

The final solution is all the values that make $(z - 9) (z - 1) = 0$ true.

$z = 9, 1$

Solve by Factoring z^2+9=10z

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