Hello!
We have the equation:
Let's solve it by the method of completing the square:
I will put the unknowns on one side and the value on the other, look:
To remove the fraction, we can divide both sides by 1/2, obtaining:
Now let's leave space to complete the square:
The value that will be added must be the same on both sides.
Remember we want to complete a square, so, let's write this expression as a product of factors:
Let's replace where is the square by 1 and solve this expression:
Notice that we can get a square on the left side when we use 1. So let's replace the square on the right side with 1 as well:
To solve this expression, we can apply the square root of both sides:
Now that the imaginary numbers part comes in, the square root of a negative number just exists in the imaginary numbers.
Let's calculate the square root of -9:
Remember that √9 = +3 or-3.
In the same way, to calculate the square root of a negative number we will follow the same steps and then replace the result with "i", in reference to imaginary numbers.
Knowing it let's finish your exercise:
As we can have a positive and a negative result, let's divide it into two results: