Question

What two numbers multiply and get 100 and add and get -29??

Answer 1

X, y - the numbers

The numbers multiply to 100.
$xy=100$

The numbers add up to -29.
$x+y=-29 \\ y=-x-29$

Substitute -x-29 for y in the first equation:
$x(-x-29)=100 \\ -x^2-29x=100 \\ -x^2-29x-100=0 \\ -x^2-4x-25x-100=0 \\ -x(x+4)-25(x+4)=0 \\ (-x-25)(x+4)=0 \\ -x-25=0 \ \lor \ x+4=0 \\ x=-25 \ \lor \ x=-4 \\ \\ y=-x-29 \\ y=-(-25)-29 \ \lor \ y=-(-4)-29 \\ y=25-29 \ \lor \ y=4-29 \\ y=-4 \ \lor \ y=-25 \\ \\ (x,y)=(-25,-4) \hbox{ or } (x,y)=(-4,-25)$

The numbers are -4 and -25.

Answer 2

I simply start by writing the possible factors of 100
1x100
2x50
4x25  this is the correct combination
therefore -25 x - 4= 100
               -25+  -4= -29