Final answer:
To find the value of c that makes the trinomial a perfect square, divide the linear coefficient by 2 and square the result. For the trinomial x² + 0.0211x, c is (0.0211/2)², resulting in the perfect square trinomial (x + 0.01055)².
Step-by-step explanation:
The student is asking to find the value of c that will make a given trinomial into a perfect square trinomial. To make a trinomial a perfect square, c should be such that the trinomial can be written in the form (ax+b)², where the middle term is twice the product of a and b, and c is the square of b. For the given trinomial x² + 0.0211x, c would be the square of half of 0.0211 since the coefficient a in front of x² is 1. Hence, c = (0.0211/2)².
To calculate c, divide 0.0211 by 2, which gives 0.01055, and then square this number to get c = 0.0001113025. The trinomial can therefore be written as a perfect square: (x + 0.01055)². To check, expand this expression to confirm it matches the original trinomial.