Answer:
4(x - [tex]\frac{1}{2}[/tex] )² = 0
Step-by-step explanation:
Given
4x² - 4x + 1 = 0
To complete the square the coefficient of the x² term must be 1
Factor out 4 from 4x² - 4x
= 4(x² - x) + 1 = 0
add/subtract ( half the coefficient of the x- term )² to x² - x
4(x² + 2(- [tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) + 1 = 0
4(x - [tex]\frac{1}{2}[/tex] )² - 1 + 1 = 0
4(x - [tex]\frac{1}{2}[/tex] )² = 0
Answer:
[tex]\huge\boxed{(2x-1)^2=0}[/tex]
Step-by-step explanation:
[tex](a-b)^2=a^2-2ab+b^2\\\\\text{We have:}\\\\4x^2-4x+1=0\\\\(2x)^2-2(2x)(1)+1^2=0\\\\\bold{a=2x,\ b=1}\\\\\text{Therefore we have:}\\\\(2x-1)^2=0[/tex]
