To solve the equation x^2 + 72 = 84, we need to isolate x.

First, subtract 72 from both sides of the equation:

x^2 + 72 - 72 = 84 - 72

This simplifies to:

x^2 = 12

Next, take the square root of both sides of the equation:

√(x^2) = √12

This gives us two possible solutions:

x = √12 or x = -√12

However, since we are given that x = 150, we can conclude that the solution to the equation is x = √12.