Question

Solve the following quadratic equation: (x−3)2−9=16
(2 points)
List the smaller solution first: {
}

Answer 1

To solve the quadratic equation \((x - 3)^2 - 9 = 16\), we first simplify the equation.

1. Start by adding 9 to both sides:

\[
(x - 3)^2 - 9 + 9 = 16 + 9
\]

This simplifies to:

\[
(x - 3)^2 = 25
\]

2. Next, take the square root of both sides:

\[
x - 3 = \pm 5
\]

3. Now we solve for \(x\) in both cases:

**Case 1:**
\[
x - 3 = 5 \implies x = 5 + 3 = 8
\]

**Case 2:**
\[
x - 3 = -5 \implies x = -5 + 3 = -2
\]

4. Therefore, the solutions are \(x = 8\) and \(x = -2\).

Listing the smaller solution first, the final answer is:

\[
\{-2, 8\}
\]