Answer :
x, y - the numbers
The numbers add up to 5 and multiply to -36.
[tex]x+y=5 \\ xy=-36 \\ \\ y=5-x \\ xy=-36 \\ \\ \hbox{substitute 5-x for y in the second equation:} \\ x(5-x)=-36 \\ 5x-x^2=-36 \\ -x^2+5x+36=0 \\ -x^2-4x+9x+36=0 \\ -x(x+4)+9(x+4)=0 \\ (-x+9)(x+4)=0 \\ -x+9=0 \ \lor \ x+4=0 \\ x=9 \ \lor \ x=-4 \\ \\ y=5-x \\ y=5-9 \ \lor \ y=5-(-4) \\ y=-4 \ \lor \ y=9 \\ \\ (x,y)=(9,-4) \hbox{ or } (x,y)=(-4,9)[/tex]
The numbers are -4 and 9.
The numbers add up to 5 and multiply to -36.
[tex]x+y=5 \\ xy=-36 \\ \\ y=5-x \\ xy=-36 \\ \\ \hbox{substitute 5-x for y in the second equation:} \\ x(5-x)=-36 \\ 5x-x^2=-36 \\ -x^2+5x+36=0 \\ -x^2-4x+9x+36=0 \\ -x(x+4)+9(x+4)=0 \\ (-x+9)(x+4)=0 \\ -x+9=0 \ \lor \ x+4=0 \\ x=9 \ \lor \ x=-4 \\ \\ y=5-x \\ y=5-9 \ \lor \ y=5-(-4) \\ y=-4 \ \lor \ y=9 \\ \\ (x,y)=(9,-4) \hbox{ or } (x,y)=(-4,9)[/tex]
The numbers are -4 and 9.
