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:

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