First there are equations that are solved by factoring.
Easy example:- x^2 + 2x + 8 = 0
You need to find 2 numbers whose product = last number 8 and when added gives the coefficient of x ( that is 2)
+4 and +2 will do this so the factors are
(x + 4)(x + 2) = 0
Now either x + 4 = 0 or x + 2 = 0
solving these 2 simple equations we get the answer:-
x = -4 , -2.
If we had a number before the term in x^2 its more complicated:-
2x^2 + 5x - 7 = 0
First multiply coefficient of x by the last term - 7:-
2 * -7 = -14
Now we need 2 factors of -14 which gives us the middle coefficient + 5.
+7 and -2 look good so we write:-
2x^2 - 2x + 7x - 7 = 0
Now we factor by grouping the first 2 and the last 2 terms:-
2x(x - 1) + 7(x - 1) = 0
(x - 1) is common to both parts so we have:-
(2x + 7)(x - 1) = 0
Now we can solve this
2x + 7 = 0 or x - 1 = 0
x = 3.5, 1
Other types of quadratic are solved by the quadratic formula or by completing the square.
If you want some practice try solving:-
1. x^2 + 2x + 24 = 0
2. 3x^2 + 3x -18 = 0