Aus Online Mathematik Brückenkurs 1

In this exercise we can use the technique for writing equations in factorized form. Consider in our case the equation

\displaystyle (x+7)(x+7)=0\,\textrm{.}

This equation has only \displaystyle x=-7 as a root because both factors become zero only when \displaystyle x=-7. In addition, it is an second-degree equation, which we can clearly see if the left-hand side is expanded,

\displaystyle (x+7)(x+7) = x^{2}+14x+49\,\textrm{.}

Thus, one answer is the equation \displaystyle x^{2}+14x+49=0\,.

Note: All second-degree equations which have \displaystyle x=-7 as its sole root can be written as

\displaystyle ax^{2}+14ax+49a=0\,,

where a is a non-zero constant.