Solve the following quadratic equation by completing the square m… - Vidyadip

Question

Solve the following quadratic equation by completing the square method
$9 x^2-12 x+4=0$

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Answer

$
\begin{aligned}
& 9 x^2-12 x+4=0 \\
& x^2-\frac{12 x}{9}+\frac{4}{9}=0 \quad \ldots(\text { Dividend by } 9) \\
& x^2-\frac{4 x}{3}=\frac{-4}{9} \\
& \text { Add }\left[\frac{1}{2}\left(\frac{4}{3}\right)\right]^2 \text { on both sides } \\
& x^2-\frac{4 x}{3}+\left(\frac{2}{3}\right)^2=-\frac{4}{9}+\left(\frac{2}{3}\right)^2 \\
& \left(x-\frac{2}{3}\right)^2=-\frac{4}{9}+\frac{4}{9} \\
& \left(x-\frac{2}{3}\right)^2=0 \\
& \Rightarrow x-\frac{2}{3}=0 \\
& x=\frac{2}{3}
\end{aligned}
$
The solution is $\frac{2}{3}$

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