James is four years younger than Austin. If three times James' age is increased by the square of Austin's age, the result is 28. Find the ages of James and Austin.

**x = Austin's age**

x - 4 = James' age

x - 4 = James' age

3(x - 4) + x² = 28 {three times James' age is increased by the square of Austin's, result is 28}

3x - 12 + x² = 28 {used distributive property}

x² + 3x - 40 = 0 {subtracted 28 from each side}

(x + 8)(x - 5) = 0 {factored into two binomials}

x + 8 = 0 or x - 5 = 0 {set each factor equal to 0}

x = -8 or x = 5 {solved each equation for x}

x = 5 {age cannot be negative}

x - 4 = 1 {substituted 5, in for x, into x - 4}

**Austin is 5 and James is 1**

*- Algebra House*