Processing Math: Done

From Förberedande kurs i matematik 1

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

(x+7)(x+7)=0.

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

(x+7)(x+7)=x2+14x+49.

Thus, one answer is the equation x2+14x+49=0.

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

ax2+14ax+49a=0

where a is a non-zero constant.