2x^2-6x+5 can be written in the form a(x -b)^ 2 + c where a, b and c are positive numbers. Find a,b and c.

In order to solve this problem we must first complete the square. To complete the square we need to factorise the equation to get the coefficient of x to be 1. This gives: 2(x^2-3x)+5. We then need to complete the square for x^2-3x. This gives: 2((x-1.5)^2-(1.5)^2)+5=2((x-1.5)^2-2.25)+5. [When completing the square we need to half the coefficient of x and minus it from x^2, we then change the x^2 to x and square this. We then minus the value of the coefficient squared from the squared brackets.] We finally need to simplify: 2((x-1.5)^2-2.25)+5=2(x-1.5)^2-4.5+5=2(x-1.5)^2+0.5. So from the initial question this gives a=2, b=1.5, c=-0.5.