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

Question

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Answer 1

To solve the quadratic equation \((x + 3)^2 = 36\) using square roots, follow these steps:

1. Take the square root of both sides of the equation: \[ \sqrt{(x + 3)^2} = \sqrt{36} \]

2. This simplifies to: \[ x + 3 = 6 \quad \text{or} \quad x + 3 = -6 \]

3. Now, solve for \(x\) in each case.

   For the first equation: \[ x + 3 = 6 \] \[ x = 6 - 3 = 3 \]

   For the second equation: \[ x + 3 = -6 \] \[ x = -6 - 3 = -9 \]

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

In conclusion, the solutions are: \[ \boxed{3} \quad \text{and} \quad \boxed{-9} \]