Question

1/4 - ( 2x + 1/2 ) ^2 = 0 

 

Answer 1

\(\dfrac{1}{4}-\left(2x+\dfrac{1}{2}\right)^2=0\\ \Rightarrow\left(2x+\dfrac{1}{2}\right)^2=\dfrac{1}{4}\\ \Rightarrow\left(2x+\dfrac{1}{2}\right)^2=\left(\dfrac{1}{2}\right)^2\\ \Rightarrow\left[{}\begin{matrix}2x+\dfrac{1}{2}=\dfrac{1}{2}\\2x+\dfrac{1}{2}=-\dfrac{1}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=0\\2x=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{2}\end{matrix}\right.\)

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