Question

Which two numbers add up to 6 and muliply to -126

Answer 1

xy=-126
x+y=6
minus x

y=6-x
sub
x(6-x)=-126
6x-x^2=-126
minus (6x-x^2) both sides
0=x^2-6x-126

in form
ax^2+bx+c=0
x=
`\frac{ -b+/-\sqrt{b^(2)-4ac} }{2a}`

a=1
b=-6
c=-126

x=
`\frac{ -(-6)+/-\sqrt{(-6)^(2)-4(1)(-126)} }{2(1)}`
x=
`( 6+/-√(36+504) )/(2)`
x=
`( 6+/-√(540) )/(2)`
x=
`( 6+/-6√(150) )/(2)`
x=
`3+/-3√(150)`


the numbers are

`3+3√(150)` and
`3-3√(150)`