Answer
${{x}^{2}}+\frac{3}{5}x+\frac{9}{100}={{\left( x+\frac{3}{10} \right)}^{2}}$
Work Step by Step
${{x}^{2}}+\frac{3}{5}x$
To complete the square, convert half of the coefficient $x$ and then square the number of the outcome, and add the complete square to the expression.
Rewrite the given term and find the half of the coefficient $x$; that is $\frac{3}{5}$.
$\begin{align}
& \frac{\frac{3}{5}}{2}=\frac{3}{5}\times \frac{1}{2} \\
& =\frac{3}{10}
\end{align}$
The square of $\frac{3}{10}$ is equal to $\frac{9}{100}$.
That is,
${{\left( \frac{3}{10} \right)}^{2}}=\frac{9}{100}$
Add $\frac{9}{100}$ to complete the square.
Thus,
${{x}^{2}}+\frac{3}{5}x+\frac{9}{100}={{\left( x+\frac{3}{10} \right)}^{2}}$
Therefore, the true equation is ${{x}^{2}}+\frac{3}{5}x+\frac{9}{100}={{\left( x+\frac{3}{10} \right)}^{2}}$.
