To solve the equation 9(2x-4)² + 2 = 38, follow these steps:
1. Start with the original equation:
9(2x-4)² + 2 = 38
2. Subtract 2 from each side to isolate the squared term:
9(2x-4)² = 36
3. Divide each side by 9 to simplify the equation:
(2x-4)² = 4
4. Rewrite the equation with a rational exponent (raise each side to the 1/2 power to eliminate the square):
(2x-4)^(2) = 4^(1)
5. Solve for x by taking the square root of both sides:
2x-4 = ±√4
6. Simplify the square root of 4:
2x-4 = ±2
7. Solve for x by considering both positive and negative square roots:
For x with the positive square root: 2x-4 = 2
For x with the negative square root: 2x-4 = -2
8. Solve for x in each case:
For the positive square root: 2x = 6 -> x = 3
For the negative square root: 2x = 2 -> x = 1
Therefore, the solutions for x are x = 3 and x = 1.
