Final answer:
The equation (x-7)² = 49 can be solved by taking the square root of both sides, leading to two solutions: x = 14 and x = 0.
Step-by-step explanation:
The solutions to the equation (x-7)² = 49 involve recognizing that the left side of the equation is a perfect square. To solve this equation, take the square root of both sides:
√(x-7)² = √49
x - 7 = ±7
This yields two solutions when solving for x:
x - 7 = 7 ==> x = 14
x - 7 = -7 ==> x = 0
Therefore, the two solutions for the equation are x = 14 and x = 0.
To verify the results, these solutions can be substituted back into the original equation to ensure that the equality holds true, which would indicate that the solutions are correct.