Question

How do you solve using completing the square method `x^2+2x-3=0`?

Answer 1

(x-1)(x+3)

Explanation:

There is no real method for this except just working it out in your head on which to brackets multiply to give `x^2+2x-3` except the quadratic formula which is good if they don't go into brackets easily `(-b sqrt(b^2-4(a)(c)))/(2a)` where a= `x^2` b= `2x` and c=`3`

Answer 2

`x=1color(white)("XX")orcolor(white)("XX")x=-3`
`color(white)("XXX")`(see below for "completing the square method" of solution)

Explanation:

Given `x^2+2x-3=0`

Completing the Square
A squared binomial `(x+a)^2=x^2+2ax+a^2`

If `x^2+2x` are the first two terms of such a squared binomial
then `a=1` (and `a^2=1`)

We can add `color(red)(1)` to complete the square but to keep the the equation correct we will need to subtract `color(red)(1)` again.

`x^2+2xcolor(red)(+1) -3 color(red)(-1)=0`

`(x+1)^2 -4=0`

`(x+1)^2=4`

`(x+1) = +-2`

`x=-1+2=1color(white)("XX")orcolor(white)("XX")x=-1-2=-3`