Solve for x using the quadratic formula.
(Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.
x^2 - 12x + 52 = 0
To solve the quadratic equation x^2 - 12x + 52 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 1, b = -12, and c = 52. Plugging in these values, we have:
x = (-(-12) ± √((-12)^2 - 4(1)(52))) / 2(1)
x = (12 ± √(144 - 208)) / 2
x = (12 ± √(-64)) / 2
The expression √(-64) indicates an imaginary number since the square root of any negative number is not a real number. Simplifying this, we have:
x = (12 ± 8i)/2
x = 6 ± 4i
So, the solutions to the equation x^2 - 12x + 52 = 0 are x = 6 + 4i and x = 6 - 4i.