Having a hard time trying to figure this problem out. When it comes to the partial faction decomposition please show all the work. Especially, if there is fractions involved. If all work isn't shown will not upvote. Trying to see where my calculations are off. Please show legible work. Thanks a ton.

( 1 point ; Use the Laplace transform to solve the following initial value problem ." * " + 10*' + 25* = 0 $ ( 0 ) = - 6, *' ( 0) = 3 a. Using I' for the Laplace transform of wit ) , i.e ., I' _ LLY[Ell , find the equation you get by taking the Laplace transform of the differential equation = 0 Do. Solve for * ( s ) = C. write the above answer in its partial fraction decomposition , !Is) = That (ital * ( s ) = + J. Now, by inventing the transform , find * (t ) =