SOLUTION: 5x(squared)=4x(squared)-4x

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 5x(squared)=4x(squared)-4x      Log On


   

Question 198545: 5x(squared)=4x(squared)-4x
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given: system%285x%5E2=4x%5E2-4x%29

Continuing,
5x%5E2-4x%5E2=4x=0
x%5E2%2B4x=0

We complete the square to get the vertex;
%28x%5E2%2B4x%2Bhighlight%284%29%29-highlight%284%29=0, take half of the middle constant, then squared = %281%2F2%29%284%29=2%5E2=highlight%284%29

Then "add" and also "subtract" to the eqn, so it won't affect the operation:

%28x%2B2%29%5E2-4=0 via vertex form, y=a%28x-h%29%5E2%2Bk, wheresystem%28h=red%28x%29%2Ck=red%28y%29%29
So the vertex, red%28x=-2%29, red%28y=-4%29 ---> (-2,-4)


For the x-Intercept:
Continuing the Eqn,
x%5E2%2B4x=0
x%28x%2B4%29=0
red%28x=0%29; red%28x=-4%29



Thank you,
Jojo