Final answer:
Using the quadratic formula on x² - 4x + 4 = 0 with coefficients a=1, b=-4, c=4 yields a single real solution, x = 2, since the discriminant is zero.
Step-by-step explanation:
To solve the quadratic equation x² - 4x + 4 = 0 using the quadratic formula, we first identify the coefficients a, b, and c from the equation ax² + bx + c = 0. In this case, a = 1, b = -4, and c = 4. The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in our coefficients, we have:
x = (-(-4) ± √((-4)² - 4(1)(4))) / (2(1))
x = (4 ± √(16 - 16)) / 2
x = (4 ± √(0)) / 2
x = (4 ± 0) / 2
Therefore, x = 4 / 2 = 2
Since the discriminant (b² - 4ac) is zero, there is only one real solution to the equation, and it is x = 2.