Solve Quadratic Equations(Completing the Square)

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**Answer**

$x^{2}-5x+4=0$

or, $x^{2}-5x+4-4=-4$

or, $x^{2}-5x=-4$

or, $x^{2}-5x+\frac{25}{4}=-4+\frac{25}{4}$

or, $x^{2}-5x+\frac{25}{4}=\frac{9}{4}$

or, $\left(x-\frac{5}{2}\right)^2=\left(\frac{3}{2}\right)^2$

or, $x-\frac{5}{2}=\pm\frac{3}{2}$

or, $x =\pm\frac{3}{2}-\frac{5}{2}$

or, $x=-1$ and $x=-4$

There are two distinct solutions given by $x = -1$ and $x = -4$