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'll first simplify it:

1. Start by moving 16 to the left side of the equation:
\[
(x - 3)^2 - 9 - 16 = 0
\]
Which simplifies to:
\[
(x - 3)^2 - 25 = 0
\]

2. Now, we can rewrite the equation:
\[
(x - 3)^2 = 25
\]

3. Next, take the square root of both sides:
\[
x - 3 = 5 \quad \text{or} \quad x - 3 = -5
\]

4. Solving these two equations:
- For \(x - 3 = 5\):
\[
x = 5 + 3 = 8
\]
- For \(x - 3 = -5\):
\[
x = -5 + 3 = -2
\]

Thus, the solutions to the equation are \(8\) and \(-2\).

Now, listing the smaller solution first, we have:
\[
\{-2, 8\}
\]