Question 910622

1/x+1/(x+13)=1/29
(29*x*(x+13))/x+(29*x*(x+13))/(x+13)=(29*x*(x+13))/29
(29*(x+13))+29*x=x*(x+13)
29*x+377+29*x=x^2+13*x
58*x+377=x^2+13*x
x^2-45*x-377=0
Can it be factored?
What factors of -377 add up to -45?
Nevertheless, we will complete the square
x^2-45*x=377
Add it.
x^2-45*x+(-45/2)=377+(-45/2)
Square it.
x^2-45*x+(2025/4)=377+(2025/4)
x^2-45*x+(506.25)=377+(506.25)
x^2-45*x+(506.25)=883.25
(x-22.5)^2=883.25
(x-22.5)^2=883.25
We will continue.
x+-22.5=(+-)29.7195222
x=22.5(+-)29.7195222
Positive useful answer:
x=22.5+29.7195222
One worker is x=52.2195222
x+13=13+52.2195222
x+13=65.2195222
Other worker =65.2195222
check
1/x+1/(x+13)=1/29
1/52.2195222+1/(52.2195222+13)=1/29
1/52.2195222+1/65.2195222=1/29
0.19149926e-1+0.15332832e-1=0.34482759e-1
0.34482759e-1=0.34482759e-1
ok

Useless answer:
x=22.5-29.7195222
Useless answer is x=-7.2195222
 x =-7.2195222
 This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results