SOLUTION: Begin with ax^2 + bx + c = 0 and derive the quadratic formula by completing the square then solve x = -2 - 3x^2 by using the quadratic formula

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Begin with ax^2 + bx + c = 0 and derive the quadratic formula by completing the square then solve x = -2 - 3x^2 by using the quadratic formula      Log On


   

Question 65841This question is from textbook An Incremental Development
: Begin with ax^2 + bx + c = 0 and derive the quadratic formula by completing the square
then solve x = -2 - 3x^2 by using the quadratic formula This question is from textbook An Incremental Development

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Begin with ax^2 + bx + c = 0 and derive the quadratic formula by completing the square
ax%5E2%2Bbx%2Bc=0
ax%5E2%2Fa%2Bbx%2Fa%2Bc%2Fa=0%2Fa
x%5E2%2B%28b%2Fa%29x%2Bc%2Fa=0
x%5E2%2B%28b%2Fa%29x%2Bc%2Fa-c%2Fa=0-c%2Fa
x%5E2%2B%28b%2Fa%29x=-c%2Fa
x%5E2%2B%28b%2Fa%29x%2B%28b%2F2a%29%5E2=%28b%2F2a%29%5E2-%28c%2Fa%29
%28x%2Bb%2F2a%29%5E2=b%5E2%2F4a%5E2-c%2Fa
%28x%2Bb%2F2a%29%5E2=b%5E2%2F4a%5E2-4ac%2F4a%5E2
%28x%2Bb%2F2a%29%5E2=%28b%5E2-4ac%29%2F4a%5E2
sqrt%28x%2Bb%2F2a%29%5E2%29=%2B-sqrt%28%28%28b%5E2-4ac%29%2F4a%5E2%29%29
x%2Bb%2F2a=%2B-sqrt%28b%5E2-4ac%29%2F2a
x%2Bb%2F2a-b%2F2a=-b%2F2a%2B-sqrt%28b%5E2-4ac%29%2F2a
highlight%28x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a%29
then solve x = -2 - 3x^2 by using the quadratic formula
3x%5E2%2Bx%2B2=-2%2B2-3x%5E2%2B3x%5E2
3x%5E2%2Bx%2B2=0
a=3, b=1, c=2
x=%28-1%2B-sqrt%28%281%29%5E2-4%283%29%282%29%29%29%2F%282%283%29%29
x=%28-1%2B-sqrt%281-24%29%29%2F6
x=%28-1%2B-sqrt%28-23%29%29%2F6 If you aren't doing complex numbers yet, you can stop here and say that there is no real number solution. If you are, remember that the sqrt(-1)=i:
highlight%28x=%28-1%2B-sqrt%2823%29i%29%2F6%29
Happy Calculating!!!