Question

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

Answer 1

To solve the quadratic equation \((x + 3)^2 = 36\), we start by taking the square root of both sides.

1. Take the square root of both sides:
\[
\sqrt{(x + 3)^2} = \sqrt{36}
\]
This simplifies to:
\[
|x + 3| = 6
\]
(since the square root function outputs the absolute value).

2. Now, we can split this absolute value equation into two separate equations:
\[
x + 3 = 6 \quad \text{or} \quad x + 3 = -6
\]

3. Solve each equation separately.

For the first equation:
\[
x + 3 = 6
\]
Subtracting 3 from both sides:
\[
x = 6 - 3 = 3
\]

For the second equation:
\[
x + 3 = -6
\]
Again, subtracting 3 from both sides:
\[
x = -6 - 3 = -9
\]

4. Thus, the solutions to the equation \((x + 3)^2 = 36\) are:
\[
x = 3 \quad \text{and} \quad x = -9
\]

The final answers are:
\[
x = 3 \quad \text{and} \quad x = -9
\]