Solution 2.3:5a
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
\displaystyle \left( x+7 \right)\left( x+7 \right)=0
This equation has only
\displaystyle x=-\text{7}
as a root because both factors become zero only when
\displaystyle x=-\text{7}. In addition, it is an second-degree equation, which we can clearly see if the left-hand side is expanded:
\displaystyle \left( x+7 \right)\left( x+7 \right)=x^{2}+14x+49
Thus, one answer is the equation
\displaystyle x^{2}+14x+49=0.
NOTE: All second-degree equations which have \displaystyle x=-\text{7} as a root can be written as
\displaystyle ax^{2}+14ax+49a=0
where
\displaystyle a
is a non-zero constant.
