Solving a quadratic equation by completing the square

Once the middle term is not an even number I get very confused.

This is what I have so far:

x^2 + 5x + 5 = 0

x^2 + 5x + (5/2)^2 = -5 = (5/2)^2

(x + 5/2)^2 = -5 + 25/4

(x + 5/2) = -20/4 + 25/4 = 5/4

I don't know if I am on the right track or doing completely wrong.

Re: Solving a quadratic equation by completing the square

You are completely on the right track except the last line

x+5/2 = sqrt(5)/2 or x+5/2 = -sqrt(5)/2

Re: Solving a quadratic equation by completing the square

Hello,

You might find it less confusing if you complete the square first and then solve for$\displaystyle x$.

$\displaystyle x^2 +5x+5 = 0$

$\displaystyle (x + \dfrac{5}{2})^2 - (\dfrac{5}{2})^2 +5 = 0$

$\displaystyle (x + \dfrac{5}{2})^2 - \dfrac{25}{4} +\dfrac {20}{4} = 0$

$\displaystyle (x + \dfrac{5}{2})^2 - \dfrac{5}{4} = 0$

Now solve for$\displaystyle x$.