SOLUTION: solve this by using quadratic formula: -(l+m)-lx^2+(2l+m)x=0,l not equal to zero

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: solve this by using quadratic formula: -(l+m)-lx^2+(2l+m)x=0,l not equal to zero      Log On


   

Question 1132331: solve this by using quadratic formula:
-(l+m)-lx^2+(2l+m)x=0,l not equal to zero
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Try changing one of the variables so that is clear than it is not equal to 0. You do not want to say 1 is not equal to zero.

-(L+m)-Lx^2+(2L+m)x=0

-%28L%2Bm%29-Lx%5E2%2B%282L%2Bm%29x=0

-Lx%5E2%2B%282L%2Bm%29x-%28L%2Bm%29=0

Lx%5E2-%282L%2Bm%29x%2B%28L%2Bm%29=0
Just apply the general solution formula to this.

for variable x in quadratic equation ax%5E2%2Bbx%2Bc=0, solutions for x are
x=%28-b%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29.

Your example will give this according to this formula,
x=%28-2L-m%2B-+sqrt%28%282L%2Bm%29%5E2-4L%28L%2Bm%29%29%29%2F%282L%29
Simplify this as much as possible.
---


What can you do with the radical expression?
sqrt%28%282L%2Bm%29%5E2-4L%28L%2Bm%29%29
sqrt%284L%5E2%2B4mL%2Bm%5E2-4L%5E2-4mL%29
sqrt%284L%5E2-4L%5E2%2B4mL-4mL%2Bm%5E2%29
You should have no trouble from here. You continue and finish!