# Completing the square

• Mar 20th 2013, 09:33 AM
Krislton
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! (Giggle)

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 :)
• Mar 20th 2013, 09:41 AM
Plato
Re: Completing the square
Quote:

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.\$
• Mar 20th 2013, 10:24 AM
HallsofIvy
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 [itex]k^2[/itex] and 7 to both sides of the equation.