How do you solve #3x^2+8x=9+2x#?

1 Answer

So, to start solving this quadratic equation we can solve the like terms together. Like,

  • So, this will give us:-
  • For making the calculations for this equation more simple you can take 3 common from the whole equation which will give us:-
  • Which will give us:-
  • Now, we can apply the method of completing the square in this quadratic equation. So, the first step is to take the constant term to the other side. So this will give us,
  • Now, we will add a number to complete the square. We will add a number to both the sides by doing the half of the constant of the middle term and squaring it.
    So, the half of the constant of the middle term is 1 and then squaring it will give us 1. Now we will add 1 to both sides:-
    #x^2+2x+1= 3+1#
  • #x^2+2x+1=4#
  • Now, we can complete the square as,
    Then we can square root both the sides to get rid of this square and square rooting both the sides will give us:
    So the first zero is,
    And the second zero is,
    x+1= -4