Answer:
(2 ± i√10) / 2 which is the third option
Step-by-step explanation:
The given expression is:
2x^2 = 4x - 7
This can be rewritten as:
2x^2 - 4x + 7 = 0
The general form of the quadratic equation is:
ax^2 + bx + c = 0
Comparing the general form with the one we have, we can find that:
a = 2
b = -4
c = 7
The quadratic formula to get the roots is shown in the attached image.
Using this formula, we will find that:
b^2 - 4ac = (-4)^2 - 4(2)(7) = -40
This means that the roots would contain an imaginary part.
either:
x = (4+√-40) / 2(2) = (4+2i√10) / 4 = (2 + i√10) / 2
Or:
x = (4-√-40) / 2(2) = (4-2i√10) / 4 = (2 - i√10) / 2
This means that:
x = (2 ± i√10) / 2
Hope this helps :)