Final answer:
To solve the equation 3x² = 6x - 1, rearrange it to 3x² - 6x + 1 = 0 and use the quadratic formula to find the solutions.
Step-by-step explanation:
To solve the equation 3x² = 6x - 1, we can rearrange it to 3x² - 6x + 1 = 0. This is a quadratic equation in the form ax² + bx + c = 0, where a = 3, b = -6, and c = 1. To solve for x, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Plugging in the values, we get:
x = (-(-6) ± √((-6)² - 4(3)(1))) / (2(3))
x = (6 ± √(36 - 12)) / 6
x = (6 ± √(24)) / 6
x = (6 ± 2√6) / 6
Now we can simplify the equation:
x = 1 ± √6 / 3
So the solutions to the equation are x = (1 + √6) / 3 and x = (1 - √6) / 3.