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 can follow these steps:

1. Take the square root of both sides: \[ \sqrt{(x+3)^2} = \sqrt{36} \] This gives us: \[ x + 3 = 6 \quad \text{or} \quad x + 3 = -6 \]

2. Solve for \(x\) in both cases:

   For the first case: \[ x + 3 = 6 \] Subtract 3 from both sides: \[ x = 6 - 3 = 3 \]

   For the second case: \[ x + 3 = -6 \] Subtract 3 from both sides: \[ x = -6 - 3 = -9 \]

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

In conclusion, the solutions are \(x = 3\) and \(x = -9\).

Answer 2

use the square roots

Answer 3

(x-6)^2=51