Solve the quadratic equation using the square root property.
left parenthesis x plus 3 right parenthesis squared equals negative 25(x+3)2=−25

To solve the equation \((x + 3)^2 = -25\) using the square root property, follow these steps:

### Step 1: Isolate the square term
The equation is already in the form \((x + 3)^2 = -25\). This matches the structure required for using the square root property.

### Step 2: Take the square root of both sides
To solve for \(x + 3\), take the square root of both sides of the equation:

\[
\sqrt{(x + 3)^2} = \sqrt{-25}
\]

On the left side, \(\sqrt{(x + 3)^2} = x + 3\).

However, on the right side, \(\sqrt{-25}\) involves an imaginary number since the square root of a negative number is imaginary. We rewrite this as:

\[
\sqrt{-25} = 5i
\]

Thus, the equation becomes:

\[
x + 3 = \pm 5i
\]

### Step 3: Solve for \(x\)
Now solve for \(x\) by subtracting 3 from both sides:

\[
x = -3 \pm 5i
\]

### Final Answer:
The solutions are:

\[
x = -3 + 5i \quad \text{or} \quad x = -3 - 5i
\]

These are the two complex solutions to the equation.

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Would you like further details or clarifications?

### Here are 5 related questions for deeper understanding:
1. What are the steps to solve a quadratic equation using the quadratic formula?
2. How does the square root property help solve quadratic equations?
3. What is an imaginary number, and why is \(i = \sqrt{-1}\)?
4. How can you graphically represent complex solutions of quadratic equations?
5. How do real and complex solutions differ in quadratic equations?

### Tip:
When dealing with square roots of negative numbers, remember that they result in imaginary numbers, and the basic imaginary unit is \(i = \sqrt{-1}\).

Solve the quadratic equation using the square root property. (x + 3)^2 = -25

Learn how to solve the quadratic equation (x + 3)^2 = -25 using the square root property. This detailed solution explains key algebraic concepts, such as square roots and imaginary numbers, and provides step-by-step guidance. Suitable for Grades 9-12.

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