Final answer:
A perfect square trinomial will be produced when solving a quadratic equation by completing the square, which allows the equation to be solved for the variable.
Step-by-step explanation:
When solving a quadratic equation by completing the square, the kind of trinomial that will be produced is a perfect square trinomial. This is a result of manipulating the equation into the form (x + a)^2 = b, where x is the variable, a is a constant, and b is the value obtained after completing the square process. The perfect square trinomial has the characteristic that it can be factored into a binomial squared, represented as (ax)^2 + 2abx + b^2.
The process of completing the square involves adjusting the original quadratic equation ax^2 + bx + c = 0 by adding and subtracting a term to transform the left side into a perfect square trinomial. Then, the equation can be easily solved for x, providing the roots of the quadratic equation.