Question

solve to equation
square root of (z+5)^2 =6

Answer 1

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.

1. For the first case:
\[
z + 5 = 6
\]
Subtract 5 from both sides:
\[
z = 6 - 5
\]
\[
z = 1
\]

2. For the second case:
\[
z + 5 = -6
\]
Subtract 5 from both sides:
\[
z = -6 - 5
\]
\[
z = -11
\]

Thus, the solutions to the equation are:

\[
z = 1 \quad \text{and} \quad z = -11
\]