Final answer:
To find the values of x for the given quadratic equation, one should use the quadratic formula with the coefficients from the equation. After simplifying the discriminant, calculate the possible values for x which can be two, one, or none depending on the discriminant.
Step-by-step explanation:
We need to solve the quadratic equation ax² - (2a + 1)x + (a + 1) = 0 for x. To do this, we can use the quadratic formula, which states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using:
x = ∛-b ± √(b² - 4ac) / 2a
Plugging the coefficients from the given equation into the formula, we get:
x = ∛-(2a + 1) ± √((2a + 1)² - 4a(a + 1)) / (2a)
From here, we would simplify the expression under the square root and calculate the values for x. The equation could have two solutions, one solution, or no real solutions depending on the discriminant (the value under the square root).