1. ## Completing the square

Hi,

Please help me understand an exam question I had last semester. I know how to find the solution if I could use $\displaystyle b^2 = 4ac$ but I wasn't allowed to use that method and with completing the square, I would normally put the equation in unity, but it already is so I can miss that step, then take half the coefficients of the b term, move the constant to the other side of the equation, take half the coefficient of b and put it in a bracket, expand the bracket out to see what I need to add or subtract from the equation and bob should be my uncle, but I cant find the solution!

Right the questions was:

(i) By completing the square, find in terms of k the roots of the equation $\displaystyle x^2 + 2kx -7 = 0$

Any help would be greatly appreciated!

Thanks,

Kris

2. ## Re: Completing the square

Originally Posted by Krislton
Right the questions was:
(i) By completing the square, find in terms of k the roots of the equation $\displaystyle x^2 + 2kx -7 = 0$

That can written as $\displaystyle (x+k)^2=k^2+7.$

3. ## Re: Completing the square

Do you know how to multiply polynomials? In particular do you know that $\displaystyle (x+ k)^2= x^2+ 2kx+ k^2$? If so compare that with the your expression:
$\displaystyle x^2+ 2kx+ k^2$ and $\displaystyle x^2+ 2kx- 7$ You need to get $\displaystyle k^2$ and get rid of -7. You can do that by adding $k^2$ and 7 to both sides of the equation.