Originally Posted by

**angypangy** Hello

I can solve this question by using the quadratic formula but want to see how to solve by completing the square.

Equation is $\displaystyle \frac{-1}{5}x^2 + 2x - \frac{9}{2} = 0$

So my working is:

$\displaystyle \frac{-1}{5}(x^2 - 10x) - \frac{9}{2} = 0$

$\displaystyle \frac{-1}{5}(x^2 - 10x) = \frac{9}{2}$

$\displaystyle \frac{-1}{5}(x - 5)^2 - 25 = \frac{9}{2}$

$\displaystyle \frac{-1}{5}(x - 5)^2 = \frac{50}{2} + \frac{9}{2} = \frac{59}{2}$

But how do I get rid of the $\displaystyle \frac{-1}{5}$. And is the above correct so far.

My problem is that multiplying both sides by -5 means number on rhs will be negative and so no solution. But I know the curve does cross the x axis - so there is a solution. Can anyone show me the final steps to solve this using completing the square?

Angus