The sum of the square of a positive number and the square of 3 more than the number is 45. what is the number?

X= a number

sum= add
more than= add
is= equal sign
square of= multiply the # by itself

x^2 + (x+3)^2= 45
x^2 + (x+3)(x+3)= 45

x^2 + x^2 + 3x + 3x + 9 = 45
combine like terms

2x^2 + 6x + 9= 45
subtract 9 from both sides

2x^2 + 6x= 36
reduce by dividing everything by 2

x^2 + 3x= 18
subtract 18 from both sides

x^2 + 3x - 18= 0
factor
(x+6)(x-3)= 0

x+6= 0
x= -6

x-3=0
x= 3

The question asks for the POSITIVE integer, so...

ANSWER: x= 3

Hope this helped! :)