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

Question

(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:

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