Final answer:
To find the sum of all values of x for the equation √(x+3)² = 7, we solve for x to get two solutions, x = 4 and x = -10, and then add them together to get the sum, which is -6.
Step-by-step explanation:
The question asks for the sum of all values of x that satisfy the equation √(x+3)² = 7. We start by squaring both sides of the equation to eliminate the square root, which gives us (x+3)² = 49. Simplifying further, we get x+3 = ±7, which gives us two possible equations: x+3 = 7 or x+3 = -7.
Solving each equation for x gives us the following solutions:
- x = 7 - 3
- x = -7 - 3
Which simplifies to:
- x = 4
- x = -10
To find the sum of all values of x, we simply add these two solutions together:
Sum of values of x = 4 + (-10) = -6