# Thread: Manhattan Algebra Strategy Volume Hard exercise problem

1. Good post? |

## Manhattan Algebra Strategy Volume Hard exercise problem

The equation given is

a= 5b^2+ 10b + 7

Which is greater- a or b?

They say to do it by completing the square but I simply do not understand their solution! Please help me out with the easiest solution.

2. Good post? |

## Re: Manhattan Algebra Strategy Volume Hard exercise problem

Hi Ramlah ,

Did you get the solution ?

3. Good post? |

## Re: Manhattan Algebra Strategy Volume Hard exercise problem

Hey so in here, there's really two cases:

We see that a depends on b.

So if b>0, then obviously a > b.
If b<0, we see that the quadratic term 5b^2 is always positive and grows way quicker than the linear term 10b, and the final sum is helped by +7. You can test this out with the largest possible value for b, b=-1 assuming and b are integers. So a >0 and thus a>b here too.

So in the final answer, we see that a > b for both situations. So choice that says a>b is correct