To solve the equation \(\sqrt{(z+5)^2} = 6\), we first recognize that the square root of a squared term can yield both a positive and a negative result. Therefore, we can rewrite the equation as:
\[ z + 5 = 6 \quad \text{or} \quad z + 5 = -6 \]
Now we will solve each case separately.
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For the first case: \[ z + 5 = 6 \] Subtract 5 from both sides: \[ z = 6 - 5 \] \[ z = 1 \]
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For the second case: \[ z + 5 = -6 \] Subtract 5 from both sides: \[ z = -6 - 5 \] \[ z = -11 \]
Thus, the solutions to the equation are:
\[ z = 1 \quad \text{and} \quad z = -11 \]