Final answer:
The solutions to the quadratic equation x²-16x+65=0 are x = 9 and x = 7.
Step-by-step explanation:
This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = -16, and c = 65. To solve it, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Substituting the given values into the formula, we get:
x = (-(-16) ± √((-16)² - 4(1)(65))) / (2(1))
Simplifying further, we have:
x = (16 ± √(256 - 260)) / 2
x = (16 ± √(4)) / 2
x = (16 ± 2) / 2
Therefore, the solutions to the equation are x = 9 and x = 7.