Question 1086882

let's two numbers be {{{x}}} and {{{y}}}

if the sum of two number is {{{7}}}, we have

{{{x+y=7}}}...solve for {{{x}}}

{{{x=7-y}}}....eq.1

 and, if the product is {{{-60}}}, we have

{{{x*y=-60}}}...solve for {{{x}}}

{{{x=-60/y}}}....eq.2

from eq.1 and eq.2 we have


{{{7-y=-60/y}}}

{{{7y-y^2=-60}}}

{{{y^2-7y-60=0}}}....factor

{{{y^2-12y+5y-60=0}}}

{{{(y^2-12y)+(5y-60)=0}}}

{{{y(y-12)+5(y-12)=0}}}

{{{(y - 12)(y + 5) = 0}}}

solutions:

{{{(y - 12) = 0}}}=>{{{y=12}}}
{{{(y + 5) = 0}}}=>{{{y=-5}}}

now find {{{x}}}:

{{{x=7-y}}}....eq.1...if {{{y=12}}}

{{{x=7-12}}}
{{{x=-5}}}

{{{x=7-y}}}....eq.1...if {{{y=-5}}}

{{{x=7-(-5)}}}
{{{x=7+5}}}
{{{x=12}}}

so, you can choose {{{x=-5}}} and {{{y=12}}} or {{{x=12}}} and {{{y=-5}}}