# Help for Completing Square method

• July 10th 2010, 01:12 AM
moonnightingale
Help for Completing Square method
I have got the equation

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

I want to write it in this form

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

My efforts are these:-

I took the denominator

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

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)
• July 10th 2010, 01:24 AM
Sudharaka
Quote:

Originally Posted by moonnightingale
I have got the equation

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

I want to write it in this form

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

My efforts are these:-

I took the denominator

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

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,

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

Hope you can continue.
• July 10th 2010, 01:43 AM
moonnightingale
sorry it is not the required form which i want

$b/((s+a)^2+b^2)$
• July 10th 2010, 01:47 AM
Sudharaka
Quote:

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

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

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

Therefore, $\frac{10}{s^2+s+10}=\frac{10}{(s+\frac{1}{2})^2+\f rac{39}{4}}$
• July 10th 2010, 07:28 AM
moonnightingale
Thanks i have solved it