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, we can follow these steps:

1. Take the square root of both sides:

\[ \sqrt{(x + 3)^2} = \sqrt{36} \]

This simplifies to:

\[ x + 3 = \pm 6 \]

2. Now, we can solve for \(x\) by considering both the positive and negative cases:

Case 1: \[ x + 3 = 6 \] Subtracting 3 from both sides gives: \[ x = 6 - 3 \ x = 3 \]

Case 2: \[ x + 3 = -6 \] Subtracting 3 from both sides gives: \[ x = -6 - 3 \ x = -9 \]

3. Therefore, the solutions to the equation \((x + 3)^2 = 36\) are:

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

So, the final answer is: \[ x = 3 \quad \text{or} \quad x = -9 \]