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

2 Answers
Apr 18, 2016

Answer:

(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#

Apr 18, 2016

Answer:

#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#