Question

1-(2*x+1/2)^2=3/4

 

 

Answer 1

\(1-\left(2x+\dfrac{1}{2}\right)^2=\dfrac{3}{4}\\ \Leftrightarrow\left(2x+\dfrac{1}{2}\right)^2=1-\dfrac{3}{4}\\ \Leftrightarrow\left(2x+\dfrac{1}{2}\right)^2=\dfrac{4-3}{4}\\ \Leftrightarrow\left(2x+\dfrac{1}{2}\right)^2=\dfrac{1}{4}\\ \Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{1}{2}=\dfrac{1}{2}\\2x+\dfrac{1}{2}=-\dfrac{1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{1}{2}-\dfrac{1}{2}\\2x=-\dfrac{1}{2}-\dfrac{1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x=0\\2x=-1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{2}\end{matrix}\right.\)

Answer 2

\(1-\left(2x+\dfrac{1}{2}\right)^2=\dfrac{3}{4}\)

\(\Rightarrow\left(2x+\dfrac{1}{2}\right)^2=\dfrac{1}{4}\)

\(\Rightarrow\)\(\left[\begin{array}{} 2x+\dfrac{1}{2} = \dfrac{1}{2}\\ 2x+\dfrac{1}{2} = \dfrac{-1}{2} \end{array} \right.\)

\(\Rightarrow\)\(\left[\begin{array}{} 2x = 0\\ 2x = -1 \end{array} \right.\)

\(\Rightarrow\)\(\left[\begin{array}{} x=0\\ x=\dfrac{-1}{2} \end{array} \right.\)