Solving the Equation (x+3)^2  36 = 0
This equation is a quadratic equation in disguise. Let's break down how to solve it:
1. Simplifying the Equation
 Expand the square: (x+3)^2 = (x+3)(x+3) = x^2 + 6x + 9
 Substitute: Now the equation becomes: x^2 + 6x + 9  36 = 0
 Combine like terms: x^2 + 6x  27 = 0
2. Solving the Quadratic Equation
We have a standard quadratic equation now: ax^2 + bx + c = 0, where a = 1, b = 6, and c = 27. We can solve this using various methods:

Factoring:
 Find two numbers that multiply to 27 and add up to 6. These numbers are 9 and 3.
 Factor the equation: (x + 9)(x  3) = 0
 Set each factor to zero and solve:
 x + 9 = 0 => x = 9
 x  3 = 0 => x = 3

Quadratic Formula:
 The quadratic formula solves for x in any equation of the form ax^2 + bx + c = 0:
 x = (b ± √(b^2  4ac)) / 2a
 Substitute the values:
 x = (6 ± √(6^2  4 * 1 * 27)) / 2 * 1
 x = (6 ± √(144)) / 2
 x = (6 ± 12) / 2
 x = 3 or x = 9
 The quadratic formula solves for x in any equation of the form ax^2 + bx + c = 0:
3. The Solutions
Therefore, the solutions to the equation (x+3)^2  36 = 0 are x = 3 and x = 9.