QUADRATIC EQUATIONS
For a, b, c ∈ R and a ≠ 0 , if the expression with three terms ax²+bx+c can be factor out in the equation of ax²+bx+c=0 the solution set is found by following way:
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The imaginary number “i” is defined as the number whose square is -1. 
The expressions in the form of ax²+bx+c=0 are called quadratic
equations.
a, b and c are known values. a can't be 0.
"x" is the variable or unknown.
The "solutions" to the Quadratic Equation are where it is equal to zero. They are also called "roots", or sometimes "zeros"
There are usually 2 solutions (as shown in this graph).
To find the solution we can use the special Quadratic Formula
The ± means there are two answers:
This is called the discriminant.
When it is 0 there are two equal roots such that
When b2 − 4ac is positive, there are two distinct real roots such that
When it is negative there is no real root and the solution set is empty on R.
EXAMPLE: Solve 5x^2 + 2x + 1 = 0
2) Note that the discriminant is negative:
3) Use the quadratic formula:
1) Coefficients are: a=5, b=2, c=1
4)
5) So:
Answer: x = −0,2 ± 0,4i