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.
