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: \[ \boxed{6} \quad \text{and} \quad \boxed{0} \]