Solve for z z^2+13z+22=0

$z^{2} + 13 z + 22 = 0$

Step 1

Factor $z^{2} + 13 z + 22$ 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 $22$ and whose sum is $13$ .

$2, 11$

Write the factored form using these integers.

$(z + 2) (z + 11) = 0$

Step 2

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

$z + 2 = 0$

$z + 11 = 0$

Step 3

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

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

$z + 2 = 0$

Subtract $2$ from both sides of the equation.

$z = - 2$

Step 4

Set $z + 11$ equal to $0$ and solve for $z$ .

Set $z + 11$ equal to $0$ .

$z + 11 = 0$

Subtract $11$ from both sides of the equation.

$z = - 11$

Step 5

The final solution is all the values that make $(z + 2) (z + 11) = 0$ true.

$z = - 2, - 11$

Solve for z z^2+13z+22=0

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