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Answer:</h3>

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Step-by-step explanation:</h3>
<u>Given equations:</u>

A) 2x² - 162 = 0
Step 1: Divide both sides by 2.
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Step 2: Take the square root of both sides (using both the positive and negative roots).

Step 3: Separate into two cases.

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B) -1/2(x - 3)² = -2
Step 1: Multiply both sides by -2.

Step 2: Take the square root of both sides (using both the positive and negative roots).

Step 3: Separate into two cases and solve each one.