Question

. Solve the following quadratic equation using square roots: 〖(x+12)〗^2=9

Answer 1

Can you please make it shorter

Answer 2

To solve the equation \((x + 12)^2 = 9\) using square roots, follow these steps:

1. Take the square root of both sides of the equation:

\[
\sqrt{(x + 12)^2} = \sqrt{9}
\]

2. This simplifies to:

\[
x + 12 = 3 \quad \text{or} \quad x + 12 = -3
\]

3. Now, solve each equation separately:

- For \(x + 12 = 3\):

\[
x = 3 - 12 = -9
\]

- For \(x + 12 = -3\):

\[
x = -3 - 12 = -15
\]

4. Therefore, the solutions to the equation \((x + 12)^2 = 9\) are:

\[
x = -9 \quad \text{and} \quad x = -15
\]

Thus, the final solutions are:

\[
\boxed{-9} \quad \text{and} \quad \boxed{-15}
\]

Answer 3

Sure! Here’s a shorter solution:

To solve \((x + 12)^2 = 9\):

1. Take the square root of both sides:

\[
x + 12 = 3 \quad \text{or} \quad x + 12 = -3
\]

2. Solve each equation:

- For \(x + 12 = 3\):
\[
x = -9
\]

- For \(x + 12 = -3\):
\[
x = -15
\]

**Final solutions:**
\[
\boxed{-9} \quad \text{and} \quad \boxed{-15}
\]