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When solving [tex]\sqrt{2x - 4} = x - 2[/tex], the equation reduces to:

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GinnyAnswer
To solve the equation [tex]\(\sqrt{2x - 4} = x - 2\)[/tex], we will isolate the square root by squaring both sides of the equation. Here’s the step-by-step process:

1. Start with the given equation:
[tex]\[ \sqrt{2x - 4} = x - 2 \][/tex]

2. Square both sides to eliminate the square root:
[tex]\[ (\sqrt{2x - 4})^2 = (x - 2)^2 \][/tex]

3. Simplify both sides after squaring:
[tex]\[ 2x - 4 = (x - 2)^2 \][/tex]

Thus, the equation reduces to:
[tex]\[ 2x - 4 = (x - 2)^2 \][/tex]

Keep in mind that this process may introduce extraneous solutions when squaring both sides, so any solutions found must be verified in the original equation.
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