Question

What two numbers add up to 7 and multiply to get -504?

Answer 1

Xy=-504
x+y=7
subtract y from both sides
x=7-y
subsitute 7-y for x
(7-y)(y)=-504
7y-y^2=-504
add (y^2-7y) to both sides
0=y^2-7y-504
use quadratic formula which is
x=$\frac{-b+/- \sqrt{ b^{2}-4ac } }{2a}$ subsitute
ax^2+bx+c
a=1
b=-7
c=-504
x=$\frac{-(-7)+/- \sqrt{ -7^{2}-4(1)(-504) } }{2(1)}$
x=$\frac{7+/- \sqrt{ 49-(-2016) } }{2}$
x=$\frac{7+/- \sqrt{ 49+2016 } }{2}$
x=$\frac{7+/- \sqrt{ 2065 } }{2}$
x=$\frac{7+/- \sqrt{ 2065 } }{2}$


x=$\frac{7+\sqrt{ 2065 } }{2}$ or x=$\frac{7- \sqrt{ 2065 } }{2}$