Firstly, we can identify 2X^{2} + 5X + 2 = 0 as a quadratic equation by the fact it is an X^{2} term, an X term and an integer term all within the same equation, and is equal to zero. To solve a quadratic equation we have 3 main methods:

1) Factorisation2) Completing the square3) The Quadratic Formula

Factorisation is usually the quickest method, but is mainly a skill in spotting the common factors, and is complicated by the **2**X^{2 } coefficient. Completing the square yields the most information about the solutions, but I would not recommend it to students unless they are very confident with algebraic manipulation of equations.

Therefore I would teach the Quadratic Formula to solve this problem. We can see that our quadratic is of the form aX^{2} + bX + c = 0 and therefore we assign our coefficients:

a = 2 , b = 5 , c = 2

Recalling that the quadratic formula is X = __- b ± ____sqr(____b__^{2}__ - 4ac) __ we can then substitute in our coefficients: 2a

X = __- 5 ± ____sqr(5__^{2}__ - 4x2x2) __ 2x2

X = __- 5 ± ____sqr(25____ - 16)__ 4

X = __- 5 ± 3 __ 4

Evaluating first with the ± symbol acting as a plus sign , and then as a minus sign we obtain:

X = -0.5 and X = -2 Two Solutions