Final answer:
The quadratic equation x² - 6x + 5 = 0 is solved using the quadratic formula, yielding two solutions: x = 5 and x = 1.
Step-by-step explanation:
To solve the quadratic equation x² - 6x + 5 = 0, we can use the quadratic formula. This is derived from an equation of the form ax² + bx + c = 0, where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant. The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a).
For this equation, a = 1, b = -6, and c = 5. Plugging these values into the quadratic formula, we get:
x = (6 ± √((-6)² - 4(1)(5))) / (2(1))
x = (6 ± √(36 - 20)) / 2
x = (6 ± √(16)) / 2
x = (6 ± 4) / 2
Therefore, the two solutions are:
- x = (6 + 4) / 2 = 5
- x = (6 - 4) / 2 = 1
So the solutions for the equation are x = 5 and x = 1.