Question

Rewrite the equation by completing the square 4x^2-4x+1=0

Answer 1

Answer:

4(x - $\frac{1}{2}$ )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(- $\frac{1}{2}$ )x + $\frac{1}{4}$ - $\frac{1}{4}$ ) + 1 = 0

4(x - $\frac{1}{2}$ )² - 1 + 1 = 0

4(x - $\frac{1}{2}$ )² = 0

Answer 2

Answer:

$\huge\boxed{(2x-1)^2=0}$

Step-by-step explanation:

$(a-b)^2=a^2-2ab+b^2\\\\\text{We have:}\\\\4x^2-4x+1=0\\\\(2x)^2-2(2x)(1)+1^2=0\\\\\bold{a=2x,\ b=1}\\\\\text{Therefore we have:}\\\\(2x-1)^2=0$