# Help for Completing Square method

• Jul 10th 2010, 12:12 AM
moonnightingale
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)
• Jul 10th 2010, 12:24 AM
Sudharaka
Quote:

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.
• Jul 10th 2010, 12:43 AM
moonnightingale
sorry it is not the required form which i want

$\displaystyle b/((s+a)^2+b^2)$
• Jul 10th 2010, 12:47 AM
Sudharaka
Quote:

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, $\displaystyle \frac{10}{s^2+s+10}=\frac{10}{(s+\frac{1}{2})^2+\f rac{39}{4}}$
• Jul 10th 2010, 06:28 AM
moonnightingale
Thanks i have solved it