Help for Completing Square method

**moonnightingale** · July 10th 2010, 12:12 AM

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)

**Sudharaka** · July 10th 2010, 12:24 AM

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.

**moonnightingale** · July 10th 2010, 12:43 AM

sorry it is not the required form which i want

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

**Sudharaka** · July 10th 2010, 12:47 AM

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

**moonnightingale** · July 10th 2010, 06:28 AM

Thanks i have solved it

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