Solve by Factoring z^2+3z=-2

$z^{2} + 3 z = - 2$

Step 1

Add $2$ to both sides of the equation.

$z^{2} + 3 z + 2 = 0$

Step 2

Factor $z^{2} + 3 z + 2$ 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 $2$ and whose sum is $3$ .

$1, 2$

Write the factored form using these integers.

$(z + 1) (z + 2) = 0$

Step 3

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

$z + 1 = 0$

$z + 2 = 0$

Step 4

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

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

$z + 1 = 0$

Subtract $1$ from both sides of the equation.

$z = - 1$

Step 5

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 6

The final solution is all the values that make $(z + 1) (z + 2) = 0$ true.

$z = - 1, - 2$

Solve by Factoring z^2+3z=-2

Related Questions

Support LCMGCF.com by disabling your adblocker.