Solve the following quatratic equations by completing square method :
`m^(2)-5m=-3`

Answer

`(5-sqrt13)/(2),(5+sqrt13)/(2)` are the roots of the given quadratic equation.

Explanation

`m^(2)-5m=-3`
`:.m^(2)-5m+3=0" "......` (Standard form)
Comparing `m^(2)-5" with "m^(2)-2mn,-2mn=-5m`
`:.n=(5)/(2):.n^(2)=(25)/(4)`
`:.m^(2)-5m+(25)/(4)` is a perfect square trinomial.
`m^(2)-5m+3=0`
`:.m^(2)-5m+(25)/(4)-(25)/(4)+3=0`
`:.(m^(2)-(5)/(2))^(2)-((25)/(4)-3)=0`
`:.(m-(5)/(2))^(2)-((25-12)/(4))=0`
`:.(m-(5)/(2))-((sqrt13)/(2))^(2)=0`
`:.(m-(5)/(3)+(sqrt(13))/(2))(m-(5)/(2)-(sqrt13)/(2))=0`
`:.m-(5)/(2)+(sqrt13)/(2)=0orm=(5)/(2)+(sqrt13)/(2)`
`:.m=(5-sqrt13)/(2)orm=(5+sqrt13)/(2)`