James is four years younger than austin. if 2 times james age is increased by the square of austins age, the result is 28. find the 2 ages. use an algebraic solution

Let the age of Austin be a, then the age of James is a-4.

"If 2 times James age is increased by the square of Austins age, the result is 28."

means: 

rearrange the quadratic equation and solve it:







add and subtract 1 to complete the square:





a+1=root 37 = 6 (approximately), so a=5 

or a+1=root 37 = -6 (approximately), so a=-7, which is not possible

The age of Austin is 5, and the age of James is 1.