Question 560249
If a quadratic equation has solutions, the quadratic expression part of the equation can be written as a product of two binomial factors and a number
{{{ax^2+bx+c=a(x-m)(x-n)}}} and {{{a(x-m)(x-n)=0}}} ,
where {{{m}}} and {{{n}}} are the solutions.
When those solutions are integers, you may be able to solve the equation by factoring.
If the two solutions are the same, you have
{{{a(x-m)^2=0}}}
That formula represents all the quadratic equations that have only {{{m}}} as a solution. There are infinitely many of them, because there are infitely many values that you can choose for {{{a}}}.
With {{{m=-2}}} , you can write {{{(x-m)^2=0}}} as
{{{(x-(-2))^2=0}}} simplifies to {{{(x+2)^2=0}}} and is equivalent to
{{{x^2+2x+1=0}}} which is probably the expected answer.