Final answer:
The quadratic formula is used to find the solutions of a quadratic equation. By substituting the values of a, b, and c into the quadratic formula, we can calculate the solutions for x in the equation x² - 3x + 1 = 0. The solutions to the equation are approximately x = 1.38 and x = 1.62.
Step-by-step explanation:
The quadratic formula is used to find the solutions of a quadratic equation. In this case, we have the equation x² - 3x + 1 = 0. By substituting the values of a, b, and c into the quadratic formula, we can calculate the solutions for x:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation, a = 1, b = -3, and c = 1. Substituting these values into the quadratic formula:
x = (-(-3) ± √((-3)² - 4(1)(1))) / (2*1)
Simplifying further:
x = (3 ± √(9 - 4))/ 2
x = (3 ± √5) / 2
Therefore, the solutions to the equation x² - 3x + 1 = 0 are approximately x = 1.38 and x = 1.62.