Final answer:
To find the solution set for the equation (5x+6)² = 2, we take the square root of both sides, which results in two possible solutions and then isolate x to find the solution set is {(±sqrt(2) - 6)/5}.
Step-by-step explanation:
To solve the equation (5x+6)² = 2, we first take the square root of both sides to eliminate the exponent. This will give us two possible solutions, because the square root of a number can be both positive and negative.
First, we have:
- sqrt((5x+6)²) = sqrt(2)
- 5x + 6 = ±√2
Once we have those, we then solve for x by subtracting 6 from both sides and then dividing by 5:
- 5x = ±√2 - 6
- x = (±(√2) - 6)/5
Therefore, the solution set is {(±(√2) - 6)/5}.