Question

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

Answer 1

To solve the quadratic equation \((x+3)^2 = 36\) using square roots, we will take the following steps:

1. **Take the square root of both sides**:
\[
x+3 = \pm \sqrt{36}
\]

2. **Simplify the square root**:
\[
x+3 = \pm 6
\]

3. **Set up two separate equations** based on the \(\pm\) sign:
- Case 1:
\[
x + 3 = 6
\]
- Case 2:
\[
x + 3 = -6
\]

4. **Solve each case**:
- For Case 1:
\[
x + 3 = 6 \implies x = 6 - 3 = 3
\]
- For Case 2:
\[
x + 3 = -6 \implies x = -6 - 3 = -9
\]

5. **Final solutions**:
The solutions to the equation \((x+3)^2 = 36\) are:
\[
x = 3 \quad \text{and} \quad x = -9
\]