Question

Solve by the Extraction of Roots method: (x-2)^(2)=49.

Answer 1

To solve (x-2)²=49, take the square root of both sides, giving x-2 = ± 7, and then solve for x to find the two solutions: x = 9 or x = -5.

Step-by-step explanation:

To solve the equation (x-2)²=49 using the Extraction of Roots method, we first take the square root of both sides. This yields two possible solutions because the square root of a positive number has both a positive and negative value. So, the square root of 49 is ± 7. We then have x-2 = 7 or x-2 = -7. Solving each equation for x gives us x = 9 or x = -5.

1. Take the square root of both sides: √(x-2)² = √49
2. Write down the positive and negative square root: x-2 = ± 7
3. Solve for x: x = 2 ± 7
4. There are two solutions: x = 9 or x = -5

Thus, the two solutions to the equation are x = 9 and x = -5.