How do you solve 14x^2+3x-2=014x2+3x2=0?

1 Answer
Jul 8, 2015

The solutions are
color(blue)(x=2/7 , x=-1/2x=27,x=12

Explanation:

14x^2 + 3x -2 = 014x2+3x2=0

We can first factorise the equation and then find the solutions :

Factorising by splitting the middle term:

14x^2 + 3x -2 = 014x2+3x2=0

14x^2 + color(blue)(7x -4x) -2 = 014x2+7x4x2=0

7x (2x+1) -2 (2x+1) = 07x(2x+1)2(2x+1)=0

color(blue)((7x -2)(2x+1) = 0(7x2)(2x+1)=0

Now, equating the factors with zero to obtain the solutions
7x -2 = 0 , color(blue)(x=2/77x2=0,x=27
2x+1 = 0 ,color(blue)( x =-1/22x+1=0,x=12