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About Quadratic1600: SQR -1 love Maths - I just do the odd maths question for fun in my spare time. My favourites vary from Probability to Quadratics and Completing the square but also equations

This is lesson 1 on completing the square. This is just a simple example to begin with and I will show harder equations in the second lesson.

This lesson will show you some examples to help with a better understanding of equations.

So lets get started

x^2 + 2x - 4 = 0

Ok so we want to get this in to the completing the square form which is (x+a)^2 + b

So our equation becomes (x+1)^2

This is because we make x^2 x and we make 2x 1 so we get (x+1)^2
Now that is equal to (x+1)(x+1) which works out as

x^2 + x + x + 1 so we then go back and say
(x+1)^2 -1 because when we worked out that equation we got an extra number out of it which was (1) so we have to subtract this (extra number) from the equation.

But we must also remember the -4 from the original equation so

(x+1)^2 -1 -4 = (x+1)^2 - 5 / That is completing the square in a very simple version and it can be used to find the vertex on a graph or in other words the roots to the equation x^2 + 2x - 4 = 0 and also the two values for x.

Firstly I will show you the vertex 
we know x + 1 = 0 so x = -1 and the other point is b which in this equation is -5 so the vertex is (-1,-5).

To find the two solutions for this equation we have to take the equation over the other side and say

(x+1)^2 -5 = 0
(x+1)^2 = 5
x + 1 = +- SQR of 5 
x = -1 +- SQR of 5 which is a surd - I will keep it in this form as we don't need the roots of the equation right now.

I hope this helped you have a better understanding of completing the square and I will do a second lesson shortly