Question

Solve the following equation by factoring. Write your answer in reduced fraction form, if necessary.22 + 11z + 28 = 0AnswerHow to enter your answer (opens in new window)На КеурKeyboard Shorz =R%3D

Answer 1

Step 1

Find two factors that when added gives us 11z and when multiplied give us 28z².

`\begin{gathered} \text{These factors are 4z and 7z} \\ 4z+7z=11z \\ 4z(7z)=28z^2 \end{gathered}`

Step 2

Replace 11z with (4z+7z)

`\begin{gathered} z^2+4z+7z+28=0 \\ \end{gathered}`

Factorize

`\begin{gathered} (z^2+4z)(+7z+28)=0 \\ Find\text{ GCF in each bracket} \\ z((z^2)/(z)+(4z)/(z))+7((7z)/(7)+(28)/(7))=0 \\ z(z+4)+7(z+4)=0 \end{gathered}`

Therefore;

`\begin{gathered} (z+4)(z+7)=0 \\ z+4=0;\text{ z=-4} \\ z+7=0;\text{ z=-7} \\ z=-4,z=-7 \end{gathered}`

Answer;

`z=-4,z=-7`