1. What is an equation?
An equation is the equality of two different expressions.
This equality is true only for a number of dinstinct values (or none) of the unknow quality.
This process of finding these values is called….

2. Solving equations -2x + 1 = 2 (4+8) + 1 -4x
One or both of the expressions may contain variables, in a linear equation they are usually indicated with an ‘x’.
Solving an equation means manipulating the expressions and finding the value of the variables.
An example might be:
-2x + 1 = 2 (4+8) x

3. Solving equations -2x + 1 = 2 (4+8) + 1 -4x -2x +4x= 2 (4+8) + 1 - 1
to solve this we have to put all the known terms on the same side and simplify them.
When we move a term from one side to an other,
we have to change its sign.
-2x +4x= 2 (4+8)
Now we find out the value of the second side and then we divide every side by 2.
2x/2 = 24/2
x= 12

4. Properties
To keep an equation equal, we must do exactly the same thing to each side of the equation. If we add (or subtract) a quantity from one side, we must add (or subtract) that same quantity from the other side. To solve this equation we would add 3 to both sides.
The equation would become x =
This becomes x = or x = 8.

5. Quadratic equations
When a quadratic expression has a particular value, we have a quadratic expression.
x2+5x+6=0
It can be written in the general form:
ax²+bx+c=0
The terms are not always given in this order and they should be arranged into the standard form.
A quadratic expression can be solved in more than one different way.

6. Solution by factorising
Consider the equation
x2+5x+6=0.
This can be factorized into
(x+2)(x+3)=0.
So the solutions must be x1=-2 and x2=-3 because when we substitute any of the two values in the given equation, we obtain zero.

7. The formula for solving a quadratic equation
Using the general quadratic equation, we can reach a formula that can solve every equation in variables x,x2.: ax²+bx+c=0
First we isolate the known term;
ax²+bx=-c
2) Then we divide all the terms by a on both sides:
x²+[(b/a)(x)]= -c/a

8. The formula for solving a quadratic equation
3) We write the term b/a as a double product:
b/a (x) =2(x) b/a
X²+2(x) (b/2a)= -(c/a)
4) We add to both sides the term (b/2a) ² ;
making this we complete the square:
X²+ b/a(x) + (b/2a)²= -(c/a) + (b/2a)²

9. The formula for solving a quadratic equation
5) The trinomiol of the first side it’s the square of the binomiol we were looking for:
(x+ b/2a) ²= - (c/a) + (b²/4a²) = ( b²- 4ac/4a²)
V(b2 - 4ac)
6) (x+b)/2a =                   a2

10. The formula for solving a quadratic equation
-b + V(b2 - 4ac)
6)x1 =                2a
-b – V(b2 – 4ac)
x2= 2a

11. The formula for solving a quadratic equation
7) These values we found out are the solutions of our equation: ax²+bx+c=0.