Solution assignment 06 Quadratic equations (abc-formula)

Solve:

$4x^2+20x+25=0$

Factorization is not easy and thus we apply the $abc$ -formula:

$x_{1,2}=\displaystyle\frac{-20\pm\sqrt{20^2-4.4.25}}{2.4}=\displaystyle\frac{-20\pm0}{8}=-\displaystyle\frac{5}{2}$

Both solutions are::

$x=-\displaystyle\frac{5}{2}$

So we have two equal or coinciding solutions.

Note that we could also have applied one of the special products:

$(a+b)^2=a^2+2ab+b^2$

When we take:

$a=2x$ and $b=5$

we could have written:

$4x^2+20x+25=(2x+5)^2$

and found the solution.

The so-called special products seem to be forgotten in recent years, but in this example they show their usefulness.