## Solving Quadratic Equations using the Square Root Property: (x+3)^2 = -16

The square root property is a valuable tool for solving quadratic equations in the form of **(ax + b)^2 = c**. This method allows us to directly isolate the variable, simplifying the solving process.

Let's walk through how to solve the equation **(x + 3)^2 = -16** using this property:

### 1. Isolate the Squared Term

Our equation is already in the desired form, with the squared term isolated on the left side.

### 2. Take the Square Root of Both Sides

The square root property states that if **a^2 = b**, then **a = ±√b**. Applying this to our equation:

√((x + 3)^2) = ±√(-16)

### 3. Simplify

Simplifying both sides:

x + 3 = ±4i

where **i** is the imaginary unit, defined as **√(-1)**.

### 4. Solve for x

Subtract 3 from both sides to isolate x:

x = -3 ± 4i

### Solution

The solutions to the equation **(x + 3)^2 = -16** are:

**x = -3 + 4i****x = -3 - 4i**

### Key Points to Remember

**Imaginary Solutions:**When the square root of a negative number arises, the solutions involve imaginary numbers.**Two Solutions:**The square root property always generates two solutions, one positive and one negative.

By understanding the square root property, we can efficiently solve a range of quadratic equations, including those with imaginary solutions.