To solve the equation \( -9 + (x - 3)^2 - 4 = -4 \), we first simplify the equation.
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Combine like terms on the left side: \[ -9 - 4 + (x - 3)^2 = -4 \] This simplifies to: \[ -13 + (x - 3)^2 = -4 \]
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Next, add 13 to both sides of the equation: \[ (x - 3)^2 = -4 + 13 \] Simplifying gives: \[ (x - 3)^2 = 9 \]
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Now, we will take the square root of both sides: \[ x - 3 = \pm 3 \]
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This gives us two possible equations:
- \( x - 3 = 3 \)
- \( x - 3 = -3 \)
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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: \[ \boxed{6} \quad \text{and} \quad \boxed{0} \]