Question

2x^2+12x-14=0 by completing the square

Answer 1

First factor 2 from the quadratic:

$2x^2+12x-14=2(x^2+6x-7)$

Now complete the square:

$x^2+6x-7=x^2+6x+9-16=(x+3)^2-16$

So we have

$2x^2+12x-14=0\implies2(x+3)^2-32=0$

$\implies2(x+3)^2=32$

Solve for x:

$(x+3)^2=\dfrac{32}2=16$

$x+3=\pm\sqrt{16}=\pm4$

$\implies x=-3+4=1\text{ OR }x=-3-4=-7$

and so the third option is correct.