Final answer:
The quadratic equation y^2 - 6y + 10 = 0 is solved using the quadratic formula, yielding two complex solutions: y = 3 + i and y = 3 - i, as the discriminant is negative.
Step-by-step explanation:
To solve the quadratic equation y2 - 6y + 10 = 0, we will use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b2 - 4ac)) / (2a)
For our equation, a = 1, b = -6, and c = 10. Substituting these values into the formula gives:
x = (6 ± √((-6)2 - 4(1)(10))) / (2(1))
x = (6 ± √(36 - 40)) / 2
x = (6 ± √(-4)) / 2
Since the discriminant (b2 - 4ac) is negative, this means we have complex solutions.
x = (6 ± 2i) / 2
x = 3 ± i
Therefore, the solutions to the equation are y = 3 + i and y = 3 - i.