Final answer:
The solutions to the equation x² - 16x + 73 = 0 are x = 8 ± 3i.
Step-by-step explanation:
This expression is a quadratic equation of the form ax² + bx + c = 0, where the constants are a = 1, b = -16, and c = 73. To solve this equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
Plugging in our values, we get:
x = (-(-16) ± sqrt((-16)^2 - 4(1)(73)))/(2(1))
Simplifying further, we have:
x = (16 ± sqrt(256 - 292))/(2)
x = (16 ± sqrt(-36))/(2)
Since we have a negative number under the square root, we know that the solutions to this equation will be complex numbers. Therefore, the solutions to the equation x² - 16x + 73 = 0 are:
x = (16 ± 6i)/2
Simplifying, we get:
x = 8 ± 3i