Solve the following for x: 2x^2-9x=5

The format of this question shows that it is a quadratic, which we can solve by factorising. We have 3 methods by which we can do this:First, we need to manipulate the equation into the form ax^2+bx+c. Subtracting 5 from each side, we see a=2, b=-9, c=-5.Now, we can use each method in turn.ASolve using the method of factors:(I'd usually use a whiteboard to explain this, as it requires a diagram)Both a and c only have one factor pair, greatly simplifying the question. We can see that the brackets must be (2x +/- 1)(x+/-5)=0. Using the original question to identify the correct signs, we get our solution of x=-0.5 or x=5. (This really does need a diagram to explain)BCompleting the square:Firstly, we need the equation in the form where a=1, so we have to divide both sides by 2 to get x^2-9/2x-5/2=0.Then, we can take the first step, of changing to the form (ax+b/2)^2-(b^2)/4+c=0.By taking everything apart from the brackets to the right hand side, we get (x-9/4)^2=121/16.Square rooting, we now have x-9/4=+/- 11/4. Solving this simply gives the same answers as before!CFinally, we can use the quadratic formula. This is more useful for fiddly equations, but can be used for any.By substituting our values into x=(-b+/-(b^2-4ac)^.5)/2a, we get the same solutions again!