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, follow these steps:

1. Take the square root of both sides:
\[
\sqrt{(x + 3)^2} = \sqrt{36}
\]

2. This gives:
\[
x + 3 = \pm 6
\]

3. Now, split it into two separate equations:
- For the positive case:
\[
x + 3 = 6
\]
Subtracting 3 from both sides, we get:
\[
x = 6 - 3 = 3
\]

- For the negative case:
\[
x + 3 = -6
\]
Subtracting 3 from both sides, we get:
\[
x = -6 - 3 = -9
\]

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