Final answer:
To solve the equation √((z+5)^2) = z+5, square both sides of the equation to eliminate the square root. Then, expand and simplify the equation, move all terms to one side, factor the quadratic equation, and solve for z then we get the solutions to the equation are z = -4 and z = -5. .
Step-by-step explanation:
To solve the equation √((z+5)^2) = z+5, we need to isolate z.
Step 1: Square both sides of the equation to eliminate the square root.
(√((z+5)^2))^2 = (z+5)^2
Simplifying the left side of the equation:
(z+5)^2 = z+5
Step 2: Expand the square on the left side of the equation.
z^2 + 10z + 25 = z + 5
Step 3: Move all the terms to one side of the equation.
z^2 + 10z - z + 25 - 5 = 0
z^2 + 9z + 20 = 0
Step 4: Factor the quadratic equation.
(z + 4)(z + 5) = 0
Step 5: Set each factor equal to zero and solve for z.
z + 4 = 0 or z + 5 = 0
z = -4 or z = -5
Therefore, the solutions to the equation are z = -4 and z = -5.