# Thread: Help for Completing Square method

1. ## Help for Completing Square method

I have got the equation

$\displaystyle 10/(s^2+s+10)$

I want to write it in this form

$\displaystyle b/((s+a)^2+b^2)$

My efforts are these:-

I took the denominator

$\displaystyle (s+a)^2+b^2$ = $\displaystyle (s+1/2)^2+9.75$

by completing square method

but now i am stuck up due to numerator

Kindly help me

And thanks to Fantastic ( i have learnt Latix as well little bit)

2. Originally Posted by moonnightingale
I have got the equation

$\displaystyle 10/(s^2+s+10)$

I want to write it in this form

$\displaystyle b/((s+a)^2+b^2)$

My efforts are these:-

I took the denominator

$\displaystyle (s+a)^2+b^2$ = $\displaystyle (s+1/2)^2+9.75$

by completing square method

but now i am stuck up due to numerator

Kindly help me

And thanks to Fantastic ( i have learnt Latix as well little bit)
Dear moonnightingale,

$\displaystyle s^2+s+10=(s+\frac{1}{2})^2-\frac{1}{4}+10$

Hope you can continue.

3. sorry it is not the required form which i want

$\displaystyle b/((s+a)^2+b^2)$

4. Originally Posted by moonnightingale
sorry it is not the required form which i want

$\displaystyle b/((s+a)^2+b^2)$
$\displaystyle s^2+s+10=(s+\frac{1}{2})^2-\frac{1}{4}+10=(s+\frac{1}{2})^2+\frac{39}{4}$

Therefore, $\displaystyle \frac{10}{s^2+s+10}=\frac{10}{(s+\frac{1}{2})^2+\f rac{39}{4}}$

5. Thanks i have solved it