z2+13z+22=0

Consider the form x2+bx+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

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

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

Set the first factor equal to 0.

z+2=0

Subtract 2 from both sides of the equation.

z=-2

z=-2

Set the next factor equal to 0.

z+11=0

Subtract 11 from both sides of the equation.

z=-11

z=-11

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