This is the problem you helped me with. I was curious, do I write the solution set as (1 + i3�ã3)/2,
(1-i3�ã3)/2
change it to the standard form first
x^2 - x + 7 = 0
a=1, b=-1, c = 7
x = (1 �} �ã(1 - 4(1)(7))/2
= (1 �} �ã-27)/2
Your answer is an imaginary number or called a complex number, you could rewrite is as
x = (1 �} 3�ã3 i)/2
To write the solution set in standard form, you started with the quadratic equation: x^2 - x + 7 = 0. You correctly identified a = 1, b = -1, and c = 7.
To find the solutions using the quadratic formula, you substituted these values into the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in a = 1, b = -1, and c = 7, we have:
x = (1 ± √((-1)^2 - 4(1)(7))) / 2(1)
Simplifying further:
x = (1 ± √(1 - 28)) / 2
x = (1 ± √(-27)) / 2
At this point, you correctly recognize that the square root of -27 is not a real number, but an imaginary number or complex number. The square root of -1 is defined as "i". So, we can rewrite the expression as:
x = (1 ± √(3i)^2)/2
Next, you simplify further:
x = (1 ± 3i√3) / 2
Finally, to express the solution set in a standard complex number form, you rewrite it as:
x = (1 + 3√3i) / 2 and x = (1 - 3√3i) / 2
So, the solution set in standard form is (1 + 3√3i) / 2 and (1 - 3√3i) / 2.