Answer:
The solutions of the given equations are -1 and 13.
Step-by-step explanation:
The given equation is
[tex]p^2-12p=13[/tex]
Subtract 13 from both the sides.
[tex]p^2-12p-13=0[/tex]
Middle term can be written as -13p+p,
[tex]p^2-13p+p-13=0[/tex]
[tex]p(p-13)+1(p-13)=0[/tex]
[tex](p+1)(p-13)=0[/tex]
Using zero product property, equal each factor equal to 0.
[tex]p+1=0\Rightarrow p=-1[/tex]
[tex]p-13=0\Rightarrow p=13[/tex]
Therefore the solutions of the given equations are -1 and 13.
