Question

Solve the following quadratic equation using square roots (x+3)^2 = 36

Answer 1

To solve the equation \((x+3)^2 = 36\) using square roots, we can follow these steps:

1. Take the square root of both sides of the equation. Remember to consider both the positive and negative roots:

\[
x + 3 = \pm 6
\]

2. Now, we can solve for \(x\) by isolating it. This gives us two scenarios to consider:

**Case 1:**

\[
x + 3 = 6
\]

Subtract 3 from both sides:

\[
x = 6 - 3
\]
\[
x = 3
\]

**Case 2:**

\[
x + 3 = -6
\]

Subtract 3 from both sides:

\[
x = -6 - 3
\]
\[
x = -9
\]

3. The solutions to the equation \((x+3)^2 = 36\) are:

\[
x = 3 \quad \text{and} \quad x = -9
\]

Thus, the final answer is:

\[
\boxed{3 \text{ and } -9}
\]