Question

Solve the following quadratic equation using square roots: −9+(x−3)2−4=−4 .

Answer 1

To solve the equation \( -9 + (x - 3)^2 - 4 = -4 \), we first simplify the equation.

1. Combine like terms on the left side:
\[
-9 - 4 + (x - 3)^2 = -4
\]
This simplifies to:
\[
-13 + (x - 3)^2 = -4
\]

2. Next, add 13 to both sides of the equation:
\[
(x - 3)^2 = -4 + 13
\]
Simplifying gives:
\[
(x - 3)^2 = 9
\]

3. Now, we will take the square root of both sides:
\[
x - 3 = \pm 3
\]

4. This gives us two possible equations:
- \( x - 3 = 3 \)
- \( x - 3 = -3 \)

5. Solve each equation for \( x \):
- For \( x - 3 = 3 \):
\[
x = 3 + 3 = 6
\]
- For \( x - 3 = -3 \):
\[
x = 3 - 3 = 0
\]

Therefore, the solutions to the equation are:
\[
\boxed{6} \quad \text{and} \quad \boxed{0}
\]