How do I complete the square?
1 Answer
Oct 23, 2015
#ax^2+bx+c = a(x+b/(2a))^2 + (c - b^2/(4a))#
The secret is that
Explanation:
Suppose you are given a quadratic equation to solve:
#2x^2-3x-2 = 0#
..which is in the form..
#ax^2+bx+c = 0# with#a = 2# ,#b=-3# and#c=-2#
#b/(2a) = -3/4#
So we find:
#2(x-3/4)^2 = 2(x^2-(2*x*3/4)+(3/4)^2)#
#=2(x^2-(3x)/2+9/16)#
#=2x^2-3x+9/8#
So:
#2(x-3/4)^2-25/8 = 2(x-3/4)^2-9/8-2#
#=2x^2-3x+9/8-9/8-2#
#=2x^2-3x-2#
So:
#2x^2-3x-2 = 0#
turns into:
#2(x-3/4)^2-25/8 = 0#
Hence:
#(x-3/4)^2 = 25/16#
So:
#x-3/4 = +-sqrt(25/16) = +-5/4#
and
#x = 3/4+-5/4#