SOLUTION: (s+1/4)(s+1/5) Multiply for an answer

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: (s+1/4)(s+1/5) Multiply for an answer      Log On


   

Question 330925: (s+1/4)(s+1/5) Multiply for an answer
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the FOIL Method,
%28s%2B1%2F4%29%28s%2B1%2F5%29=s%5E2%2Bs%2F5%2Bs%2F4%2B1%2F20
%28s%2B1%2F4%29%28s%2B1%2F5%29=s%5E2%2B%284s%29%2F20%2B%285s%29%2F20%2B1%2F20
%28s%2B1%2F4%29%28s%2B1%2F5%29=s%5E2%2B%289%2F20%29s%2B1%2F20

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28s%2B1%2F4%29%28s%2B1%2F5%29...we can write it as
%28s%2B1%2F4%29%28s%2B1%2F5%29=0
first find common denominator; for 4 and 5 it is 20, so multiply both sides by 20
%28s%2B1%2F4%29%28s%2B1%2F5%29%2A20=0%2A20
%2820s%2B%2820%2A1%29%2F4%29%2820s%2B%2820%2A1%29%2F5%29%2A20=0%2A20
%2820s%2B+5%29%2820s%2B4%29%2A20=0
%28400s%5E2%2B+80s%2B+100s+%2B20%29=0
%28400s%5E2%2B+180s+%2B20%29=0...simplify (divide both side by 10)
%2840s%5E2%2B+18s%2B2%29=0
now solve quadratic equation to find value of s which will be represent as an x in following part:
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 40%2Ax%5E2%2B18%2Ax%2B2=0 ( notice a=40, b=18, and c=2)





x+=+%28-18+%2B-+sqrt%28+%2818%29%5E2-4%2A40%2A2+%29%29%2F%282%2A40%29 Plug in a=40, b=18, and c=2




x+=+%28-18+%2B-+sqrt%28+324-4%2A40%2A2+%29%29%2F%282%2A40%29 Square 18 to get 324




x+=+%28-18+%2B-+sqrt%28+324%2B-320+%29%29%2F%282%2A40%29 Multiply -4%2A2%2A40 to get -320




x+=+%28-18+%2B-+sqrt%28+4+%29%29%2F%282%2A40%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-18+%2B-+2%29%2F%282%2A40%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-18+%2B-+2%29%2F80 Multiply 2 and 40 to get 80


So now the expression breaks down into two parts


x+=+%28-18+%2B+2%29%2F80 or x+=+%28-18+-+2%29%2F80


Lets look at the first part:


x=%28-18+%2B+2%29%2F80


x=-16%2F80 Add the terms in the numerator

x=-1%2F5 Divide


So one answer is

x=-1%2F5




Now lets look at the second part:


x=%28-18+-+2%29%2F80


x=-20%2F80 Subtract the terms in the numerator

x=-1%2F4 Divide


So another answer is

x=-1%2F4