After posting all this work, in both formats, my teacher still wants to play games and is asking me what number should be paired with -5 and what number should be paired with 2. What in the world is she talking about?

1. The product of two numbers is 10. One number is 3 more than the other number. What is the quadratic equation that models these numbers?

x(x + 3) = 10

x^2 + 3x - 10 = 0

2. Solve the quadratic equation from #1, to find the pairs of numbers.

x = -(3) +_ SQRT((3)^2) - 4(1)(-10)/2(1)

= -3 +_ SQRT(9 + 40)/2 = -3 +_ SQRT(49)/ 2

= -3 +_7/2 = -3 - 7/2, -3 + 7/2

= -10/2, 4/2 = -5, 2

x = -5, x = 2

and this additional work:

(b + 3)b = 10

b^2 + 3b = 10

b^2 + 3b -10 = 0

x = -(3) +_ SQRT((3)^2 - 4(1)(-10)/2(1)

= -3 +_ SQRT(9 + 40)/2 = -3 +_SQRT(49)/2

= -3 +_ 7/2 = -3 -7/2, -3 +7/2

= -10/2, 4/2

= -5, 2

x = -5, 2

I mean, this just seems rediculous