Question

Solve the following quadratic equation using square roots: (x+3)2=36
.(1 point)
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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:
\[
x = 3 \quad \text{or} \quad x = -9
\]