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

1 answer

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