The equation 2x² - 12x + 9 = 0 can be factored into (2x - 3)² = 0. This means that the equation has a repeated root at x = 3.
To find which of the given equations has the same solutions as 2x² - 12x + 9 = 0, we need to compare the factored form (2x - 3)² = 0 with the options provided.
Among the options given:
1. 2(x-3)² = 0 does not have the same solutions because it has a single root at x = 3, not a repeated root.
2. 2(x-6)² = 63 does not have the same solutions as it involves a different value than 0 on the right side of the equation.
3. 2(x-3)² = 9 has the same solutions as 2x² - 12x + 9 = 0 because it simplifies to (2x - 3)² = 9, which is equivalent.
4. 2(x-6)² = 27 does not have the same solutions as it involves a different value than 0 on the right side of the equation.
Therefore, the equation that has the same solutions as 2x² - 12x + 9 = 0 is 2(x-3)² = 9.
