How do you solve $14 x^{2} + 3 x - 2 = 0$ $14x^2+3x-2=0$ ?

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How do you solve $14 x^{2} + 3 x - 2 = 0$ $14x^2+3x-2=0$ ?

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Answer 1 · 2015-07-08T09:27:58

The solutions are
$x = \frac{2}{7}, x = - \frac{1}{2}$ $color(blue)(x=2/7 , x=-1/2$

Explanation:

$14 x^{2} + 3 x - 2 = 0$ $14x^2 + 3x -2 = 0$

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

Factorising by splitting the middle term:

$14 x^{2} + 3 x - 2 = 0$ $14x^2 + 3x -2 = 0$

$14 x^{2} + 7 x - 4 x - 2 = 0$ $14x^2 + color(blue)(7x -4x) -2 = 0$

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

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

Now, equating the factors with zero to obtain the solutions
$7 x - 2 = 0, x = \frac{2}{7}$ $7x -2 = 0 , color(blue)(x=2/7$
$2 x + 1 = 0, x = - \frac{1}{2}$ $2x+1 = 0 ,color(blue)( x =-1/2$

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How do you solve $14 x^{2} + 3 x - 2 = 0$ $14x^2+3x-2=0$ ?

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