Final answer:
To solve the equation (3x² - x + 4) = (x - 1), we can simplify the equation, combine like terms, and solve the resulting quadratic equation using the quadratic formula. The solutions to the equation are x = 1 and x = -2.
Step-by-step explanation:
To solve the equation (3x² - x + 4) = (x - 1), we can first simplify the equation by removing the parentheses: 3x² - x + 4 = x - 1.
Next, we can combine like terms on both sides of the equation: 3x² - x - x + 4 - 4 = x - x - 1 - 4. This simplifies to 3x² - 2x + 4 - 4 = -1.
Now, we have the quadratic equation 3x² - 2x - 1 = 0. We can solve this equation using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Plugging in the values for a, b, and c from the quadratic equation, we have x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3)). Simplifying further, we get x = (2 ± √(4 + 12)) / 6. This gives us two possible values for x: x = (2 ± √16) / 6. Simplifying again, we get x = (2 ± 4) / 6.
Finally, we can simplify the values of x: x = (2 + 4) / 6 and x = (2 - 4) / 6. This simplifies to x = 6 / 6 and x = -2 / 6. Therefore, the solutions to the equation are x = 1 and x = -2.