To solve the equation \(-9 + (x - 3)^2 - 4 = -4\), let's start simplifying it step by step.
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Combine the constant terms on the left side: \[ -9 - 4 = -13 \] So the equation becomes: \[ (x - 3)^2 - 13 = -4 \]
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Now add 13 to both sides: \[ (x - 3)^2 = -4 + 13 \] Simplifying this gives: \[ (x - 3)^2 = 9 \]
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Now take the square root of both sides: \[ x - 3 = 3 \quad \text{or} \quad x - 3 = -3 \]
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Solving the first equation: \[ x - 3 = 3 \implies x = 6 \]
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Solving the second equation: \[ x - 3 = -3 \implies x = 0 \]
Now, we have the solutions: \[ x = 6 \quad \text{and} \quad x = 0 \]
Since neither of the given answer choices match \(6\) and \(0\), let's review and solve the equation again, ensuring all calculations are correct.
Starting again from: \[ -9 + (x - 3)^2 - 4 = -4 \] Rearranged: \[ (x - 3)^2 = 9 \] Taking the square root gives solutions: \[ x = 6 \quad \text{and} \quad x = 0 \]
Given this, the response options don't reflect the correct solutions. Please check whether there is any missing information or errors in the answer choices provided.
1 answer