Question

factories 3x²-2x-6=0

Answer 1

Hey there!

Factorise

$3x {}^{2} - 2x - 6 = 0$

We can solve it with
i) quadratic formula and
ii) completing the square method.

Solve the quadratic equation ax²+bx+c =0 using

$x = \frac{ - b + - \sqrt{b {}^{2} - 4ac } }{2a}$

$x = \frac{ - ( - 2) + - \sqrt{( - 2) {}^{2} - 4 \times 3 \times ( - 6)} }{6}$

$x = \frac{2 + - \sqrt{76} }{6}$

$x = \frac{2 + - 2 \sqrt{19} }{6}$

$x = \frac{1 + - \sqrt{19} }{3}$

$x1 = \frac{1 + \sqrt{19} }{3}$

$x2 = \frac{1 - \sqrt{19} }{3}$

By completing the square method,

$3x {}^{2} - 2x - 6 = 0$

$3x {}^{2} - 2x = 6$

$x {}^{2} - \frac{2}{3} x + ( \frac{2}{6} ) {}^{2} = 2 + ( \frac{2}{6} ) {}^{2}$

$(x - \frac{2}{6} ) {}^{2} = \frac{19}{9}$

$x - \frac{1}{3} = + - \frac{ \sqrt{19} }{3}$

$x - \frac{1}{3} = \frac{ \sqrt{19} }{3}$

$x - \frac{1}{3} = - \frac{ \sqrt{19} }{3}$

$x1 = \frac{ \sqrt{19} + 1 }{3}$

$x2 = - \frac{ \sqrt{19} + 1 }{3}$

Hope it helps!