How do you solve the equation #x^2-2/3x-26/9=0# by completing the square?
1 Answer
Jan 8, 2017
Explanation:
Given:
#x^2-2/3x-26/9 = 0#
The difference of squares identity can be written:
#a^2-b^2 = (a-b)(a+b)#
Use this with
#0 = x^2-2/3x-26/9#
#color(white)(0) = x^2-2/3x+1/9-3#
#color(white)(0) = (x-1/3)^2-(sqrt(3))^2#
#color(white)(0) = ((x-1/3)-sqrt(3))((x-1/3)+sqrt(3))#
#color(white)(0) = (x-1/3-sqrt(3))(x-1/3+sqrt(3))#
Hence:
#x = 1/3+-sqrt(3)#