Question

Solve the following quadratic equation: (x−3)2−9=16
(2 points)
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Answer 1

To solve the quadratic equation \((x - 3)^2 - 9 = 16\), follow these steps:

1. Start by simplifying the equation:

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

2. Add 9 to both sides to isolate the squared term:

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

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

3. Take the square root of both sides:

\[
x - 3 = 5 \quad \text{or} \quad x - 3 = -5
\]

4. Solve for \(x\) in each case:

- For the first case:

\[
x - 3 = 5 \implies x = 5 + 3 \implies x = 8
\]

- For the second case:

\[
x - 3 = -5 \implies x = -5 + 3 \implies x = -2
\]

5. The solutions to the equation are:

\[
\boxed{8} \quad \text{and} \quad \boxed{-2}
\]