Question
Solve the following quadratic equation by factorization.
$2 x^2-2 x+\frac{1}{2}=0$
$2 x^2-2 x+\frac{1}{2}=0$
✓
Answer
$\begin{array}{l}
2 x ^2-2 x +\frac{1}{2}=0 \\
\Rightarrow 4 x ^2-4 x +1=0 \\
\Rightarrow 4 x ^2-2 x -2 x +1 \\
\Rightarrow 2 x(2 x-1)-1(2 x-1) \\
\Rightarrow(2 x-1)(2 x-1) \\
\Rightarrow 2 x-1=0 \Rightarrow x=\frac{1}{2}, \frac{1}{2}
\end{array}$
Hence $x=\frac{1}{2}, \frac{1}{2}$ are roots of the equation
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