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: \[ x = 3 \quad \text{and} \quad x = -9 \]