Answer:
The solutions are: 1 + 6i and 1 - 6i
Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
x² - 2x + 37 = 0
By comparison:
a = 1
b = -2
c = 37
Now, to get the solutions of the equation, we will use the quadratic formula shown in the attached image.
By substitution in this formula, we would find that:
either x = [tex] \frac{2+ \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 + 6i[/tex]
or x = [tex] \frac{2- \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 - 6i[/tex]
Hope this helps :)
