College Algebra, Chapter 1, 1.3, Section 1.3, Problem 52

Find all real solutions of $\displaystyle 5x^2 - 7x + 5 = 0$.


$
\begin{equation}
\begin{aligned}

5x^2 - 7x + 5 =& 0
&& \text{Given}
\\
\\
5x^2 - 7x =& -5
&& \text{Subtract 5}
\\
\\
x^2 - \frac{7x}{5} =& -1
&& \text{Divide both sides by 5 to make the coefficient of $x^2$ equal to 1}
\\
\\
x^2 - \frac{7x}{5} + \frac{49}{100} =& -1 + \frac{49}{100}
&& \text{Complete the square: add } \left( \frac{\displaystyle \frac{-7}{5}}{2} \right)^2 = \frac{49}{100}
\\
\\
\left(x - \frac{7}{10} \right)^2 =& \frac{-51}{100}
&& \text{Perfect square}
\\
\\
x - \frac{7}{10} =& \pm \sqrt{\frac{-51}{100}}
&& \text{Take the square root}

\end{aligned}
\end{equation}
$


No real solution the discriminant $b^2 - 4ac < 0$