Help! Could someone explain this?

Question

  3.)      A  mother  has  two  children  whose  ages  differ  by  5  years.    The  sum  of  the  squares   of  their  ages  is  97.    The  square  of  the  mother’s  age  can  be  found  by  writing  the   squares  of  the  children’s  ages  one  after  the  other  as  a  four-­-digit  number.    How  old  is   the  mother?   

Answer 1

x and x+5 are the children's ages

x^2+(x+5)^2=97

x^2+x^2+10x+25=97

2x^2+10x+25-97=0

2x^2+10x-72=0

x^2+5x-36=0

(x+9)(x-4)=0

x-4=0

x=4

x+5=9

the children are 4 and 9

4^2=16

9^2=81

you have two choices...

1681 or 8116

√1681=41 and  √8116=90.1

common sense tells us that the mother is 41 years old