How do you solve using completing the square method x^2+x-6=0?

1 Answer
Apr 1, 2016

Using the completing the squares method as requested.
x=2 or x=-3

Explanation:

Given
color(white)("XXX")x^2+x-6=0

Adding 6 to both sides to clear the constant from the left side
color(white)("XXX")x^2+x=6

If x^2+x are the first two terms of an expanded squared binomial
(x+a)^2=x^2+2ax+a^2
then 2a=1 and a=1/2

Therefore, in order to complete the square, we will need to add a^2=(1/2)^2 to both sides:
color(white)("XXX")x^2+xcolor(red)(+(1/2)^2)=6color(red)(+(1/2)^2)

Rewriting as a squared binomial and simplifying the right side
color(white)("XXX")(x+1/2)^2=6 1/4=25/4

Taking the square root of both sides:
color(white)("XXX")x+1/2= +-sqrt(25/4)=+-5/2

Subtracting 1/2 from both sides
color(white)("XXX")x=5/2-1/2=2color(white)("XX")orcolor(white)("XX")x=-5/2-1/2=-3