Express 2x^2-20x+53 in the form 2(x-p)^2+q , where p and q are integers. not sure how to do this..
i factorised it and got this
2(x^2-10x)+53 plz help thx
$\displaystyle 2x^2 - 20x + 53$
$\displaystyle \equiv 2(x^2 - 10x) + 53$ // Take the 2 outside of the brackets
$\displaystyle \equiv 2((x-5)^2 - 25) + 53$ // Complete the square within the brackets
$\displaystyle \equiv 2(x-5)^2 - 50 + 53$ // Take the -25 outside the brackets
$\displaystyle \equiv 2(x-5)^2 + 3$ // Gather terms
What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).
CB