To solve the equation \( \sqrt{2z - 2} = 5 \), we first square both sides to eliminate the square root:
\[ 2z - 2 = 5^2 \]
Calculating the right side:
\[ 2z - 2 = 25 \]
Next, we add 2 to both sides:
\[ 2z = 25 + 2 \]
\[ 2z = 27 \]
Now, we divide by 2:
\[ z = \frac{27}{2} = 13.5 \]
Now, we will check whether \( z = 13.5 \) satisfies the original equation:
Substituting \( z = 13.5 \) into the left side of the original equation:
\[ \sqrt{2(13.5) - 2} = \sqrt{27 - 2} = \sqrt{25} = 5 \]
Since both sides are equal, \( z = 13.5 \) is indeed the correct solution.
Therefore, the value for \( z \) that makes the equation true is
\[ \boxed{13.5} \]
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